Difference between revisions of "Geogebra/C3/Tangents-to-a-circle/English-timed"

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{| border=1
 
{| border=1
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!Time
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|'''Time'''
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!Narration
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|'''Narration'''
 
|-
 
|-
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|00.00
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|00:00
 
|Hello Welcome to this tutorial on "Tangents to a circle in Geogebra".  
 
|Hello Welcome to this tutorial on "Tangents to a circle in Geogebra".  
  
 
|-
 
|-
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|00.06
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|00:06
 
|At the end of this tutorial you will be able to Draw tangents to the circle,Understand the properties of Tangents.
 
|At the end of this tutorial you will be able to Draw tangents to the circle,Understand the properties of Tangents.
  
 
|-
 
|-
−
|00.17
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|00:17
 
|We assume that you have the basic working knowledge of Geogebra.
 
|We assume that you have the basic working knowledge of Geogebra.
  
 
|-
 
|-
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|00.22
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|00:22
 
|If not,For relevant tutorials Please visit our website http://spoken-tutorial.org.
 
|If not,For relevant tutorials Please visit our website http://spoken-tutorial.org.
  
 
|-
 
|-
−
|00.27
+
|00:27
 
|To record this tutorial, I am using Ubuntu Linux OS Version 11.10, Geogebra Version 3.2.47.0 .
 
|To record this tutorial, I am using Ubuntu Linux OS Version 11.10, Geogebra Version 3.2.47.0 .
  
 
|-
 
|-
−
|00.41
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|00:41
 
|We will use the following Geogebra tools
 
|We will use the following Geogebra tools
 
     .Tangents,
 
     .Tangents,
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|-
 
|-
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|00.58
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|00:58
 
|Let's open a new GeoGebra window.
 
|Let's open a new GeoGebra window.
  
 
|-
 
|-
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|01.01
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|01:01
 
|Click on Dash home Media Applications. Under Type Choose Education and GeoGebra.  
 
|Click on Dash home Media Applications. Under Type Choose Education and GeoGebra.  
  
 
|-
 
|-
−
|01.13
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|01:13
 
|let's define tangents to a circle.
 
|let's define tangents to a circle.
  
 
|-
 
|-
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|01.16
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|01:16
 
|Tangent is a line that touches a circle at only one point.
 
|Tangent is a line that touches a circle at only one point.
  
 
|-
 
|-
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|01.22
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|01:22
 
|The point of contact is called "point of tangency".
 
|The point of contact is called "point of tangency".
  
 
|-
 
|-
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|01.27
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|01:27
 
|For this tutorial I will use "Grid" layout instead of "Axes",Right Click on the drawing pad.
 
|For this tutorial I will use "Grid" layout instead of "Axes",Right Click on the drawing pad.
  
 
|-
 
|-
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|01.35
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|01:35
 
|uncheck "Axes" Select "Grid"  
 
|uncheck "Axes" Select "Grid"  
  
 
|-
 
|-
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|01.39
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|01:39
 
| let us draw tangent to a circle.
 
| let us draw tangent to a circle.
  
 
|-
 
|-
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|01.42
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|01:42
 
|First let us draw a circle.
 
|First let us draw a circle.
  
 
|-
 
|-
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|01.45
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|01:45
 
|Select “Circle with Center and Radius” tool from toolbar.
 
|Select “Circle with Center and Radius” tool from toolbar.
  
 
|-
 
|-
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|01.49
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|01:49
 
|Mark a point 'A' on the drawing pad.
 
|Mark a point 'A' on the drawing pad.
  
 
|-
 
|-
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|01.52
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|01:52
 
|A dialogue box opens.  
 
|A dialogue box opens.  
  
 
|-
 
|-
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|01.53
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|01:53
 
|Let's type value '3' for radius,Click OK
 
|Let's type value '3' for radius,Click OK
  
 
|-
 
|-
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|01.58
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|01:58
 
|A circle with centre 'A' and radius '3' cm is drawn.  
 
|A circle with centre 'A' and radius '3' cm is drawn.  
  
 
|-
 
|-
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|02.04
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|02:04
 
|Let's 'Move' the point 'A' & see that circle has same radius.
 
|Let's 'Move' the point 'A' & see that circle has same radius.
  
 
|-
 
|-
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|02.09
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|02:09
 
|Click on the "New point" tool,Mark a point 'B' outside the circle.
 
|Click on the "New point" tool,Mark a point 'B' outside the circle.
  
 
|-
 
|-
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|02.15
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|02:15
 
| "Select Segment between two points" tool.Join points 'A' and 'B'.A Segment AB is drawn.
 
| "Select Segment between two points" tool.Join points 'A' and 'B'.A Segment AB is drawn.
  
 
|-
 
|-
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|02.25
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|02:25
 
|Select "Perpendicular Bisector" tool, Click on the points 'A' & 'B'.Perpendicular bisector to segment 'AB'  is drawn.
 
|Select "Perpendicular Bisector" tool, Click on the points 'A' & 'B'.Perpendicular bisector to segment 'AB'  is drawn.
  
 
|-
 
|-
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|02.37
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|02:37
 
|Segment 'AB' and Perpendicular bisector intersect at a point,Click on "Intersect two objects" tool.  
 
|Segment 'AB' and Perpendicular bisector intersect at a point,Click on "Intersect two objects" tool.  
  
 
|-
 
|-
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|02.44
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|02:44
 
|Mark point of intersection as 'C' Let's Move point 'B',& 'C' how the perpendicular bisector and point 'C' move along with point 'B'.  
 
|Mark point of intersection as 'C' Let's Move point 'B',& 'C' how the perpendicular bisector and point 'C' move along with point 'B'.  
  
 
|-
 
|-
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|02.59
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|02:59
 
|How to verify 'C' is the midpoint of 'AB'?
 
|How to verify 'C' is the midpoint of 'AB'?
  
 
|-
 
|-
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|03.02
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|03:02
 
|Click on "Distance" tool. click on the points 'A' , 'C'.  'C' ,'B' Notice that 'AC' = 'CB' implies 'C' is the midpoint of 'AB'.
 
|Click on "Distance" tool. click on the points 'A' , 'C'.  'C' ,'B' Notice that 'AC' = 'CB' implies 'C' is the midpoint of 'AB'.
  
  
 
|-
 
|-
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|03.20
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|03:20
 
|Select "Compass" tool from tool bar,C lick on the points 'C', 'B'. and 'C' once again... to complete the figure.  
 
|Select "Compass" tool from tool bar,C lick on the points 'C', 'B'. and 'C' once again... to complete the figure.  
  
 
|-
 
|-
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|03.30
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|03:30
 
|Two circles intersect at two points.
 
|Two circles intersect at two points.
  
  
 
|-
 
|-
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|03.33
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|03:33
 
|Click on the "Intersect two objects" tool Mark the points of intersection as 'D' and 'E'  
 
|Click on the "Intersect two objects" tool Mark the points of intersection as 'D' and 'E'  
  
 
|-
 
|-
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|03.42
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|03:42
 
|Select "Segment between two points" tool.
 
|Select "Segment between two points" tool.
  
 
|-
 
|-
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|03.45
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|03:45
 
|Join points 'B', 'D'  and 'B' , 'E' .  
 
|Join points 'B', 'D'  and 'B' , 'E' .  
  
  
 
|-
 
|-
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|03.53
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|03:53
 
|Segments 'BD' and 'BE' are tangents to the circle 'c'?  
 
|Segments 'BD' and 'BE' are tangents to the circle 'c'?  
  
 
|-
 
|-
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|03.59
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|03:59
 
| let's explore some of the properties of these Tangents to the circle.
 
| let's explore some of the properties of these Tangents to the circle.
  
 
|-
 
|-
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|04.05
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|04:05
 
|Select "Segment between two points" tool.
 
|Select "Segment between two points" tool.
  
 
|-
 
|-
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|04.08
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|04:08
 
|Join points 'A', 'D' and 'A', 'E'.
 
|Join points 'A', 'D' and 'A', 'E'.
  
 
|-
 
|-
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|04.14
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|04:14
 
|In triangles 'ADB' and 'ABE' Segment 'AD'= segment 'AE' (radii of the circle 'c').  
 
|In triangles 'ADB' and 'ABE' Segment 'AD'= segment 'AE' (radii of the circle 'c').  
  
Line 166: Line 166:
  
 
|-
 
|-
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|04.34
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|04:34
 
|'∠ADB'= '∠BEA'  angle of the semicircle of circle 'D' Lets measure the "Angle".
 
|'∠ADB'= '∠BEA'  angle of the semicircle of circle 'D' Lets measure the "Angle".
  
 
|-
 
|-
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|04.48
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|04:48
 
|Click on the "Angle" tool... Click on the points 'A', 'D', 'B' and 'B', 'E', 'A' angles are equal.
 
|Click on the "Angle" tool... Click on the points 'A', 'D', 'B' and 'B', 'E', 'A' angles are equal.
  
 
|-
 
|-
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|05.03
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|05:03
 
|Segment 'AB' is common to both the triangles,therefore '△ADB' '≅' '△ABE' by "SAS rule of congruency"  
 
|Segment 'AB' is common to both the triangles,therefore '△ADB' '≅' '△ABE' by "SAS rule of congruency"  
  
 
|-
 
|-
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|05.20
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|05:20
 
|It implies Tangents 'BD' and 'BE' are equal!
 
|It implies Tangents 'BD' and 'BE' are equal!
 
   
 
   
 
|-
 
|-
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|05.26
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|05:26
 
|From the Algebra view, we can find that tangents 'BD' and 'BE' are equal  
 
|From the Algebra view, we can find that tangents 'BD' and 'BE' are equal  
  
 
|-
 
|-
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|05.33
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|05:33
 
|Please Notice that tangent is always at right angles to the radius of the circle where it touches,  
 
|Please Notice that tangent is always at right angles to the radius of the circle where it touches,  
 
   
 
   
Line 192: Line 192:
  
 
|-
 
|-
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|05.50
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|05:50
 
|Let us save the file now. Click on “File”>> "Save As"
 
|Let us save the file now. Click on “File”>> "Save As"
  
 
|-
 
|-
−
|05.54
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|05:54
 
|I will type the file name as "Tangent-circle" Click on "Save"
 
|I will type the file name as "Tangent-circle" Click on "Save"
  
 
|-
 
|-
−
|06.08
+
|06:08
 
|Let's state a theorem  
 
|Let's state a theorem  
 
   
 
   
 
|-
 
|-
−
|06.11
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|06:11
 
|"Angle between tangent and chord at the point of tangency, is same as an inscribed angle subtended by the same chord".  
 
|"Angle between tangent and chord at the point of tangency, is same as an inscribed angle subtended by the same chord".  
 
  Angle DFB between tangents & chord= inscribed angle FCB of the chord BF.
 
  Angle DFB between tangents & chord= inscribed angle FCB of the chord BF.
  
 
|-
 
|-
−
|06.34
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|06:34
 
|Let's verify the theorem;  
 
|Let's verify the theorem;  
  
 
|-
 
|-
−
|06.38
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|06:38
 
|Let's open a new Geogebra window.click on “File” >> "New". Let's draw a circle.
 
|Let's open a new Geogebra window.click on “File” >> "New". Let's draw a circle.
  
 
|-
 
|-
−
|06.48
+
|06:48
 
|Click on the "Circle with center through point" tool from tool bar . Mark a point 'A' as a centre and click again to get 'B'.
 
|Click on the "Circle with center through point" tool from tool bar . Mark a point 'A' as a centre and click again to get 'B'.
  
 
|-
 
|-
−
|06.59
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|06:59
 
|Select "New point" tool.Mark point'C' on the circumference  and  'D' outside the circle.  
 
|Select "New point" tool.Mark point'C' on the circumference  and  'D' outside the circle.  
  
 
|-
 
|-
−
|07.06
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|07:06
 
|Select "Tangents" tool from toolbar.click on the point 'D'... and on circumference.  
 
|Select "Tangents" tool from toolbar.click on the point 'D'... and on circumference.  
  
 
|-
 
|-
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|07.14
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|07:14
 
|Two Tangents are drawn to the circle.  
 
|Two Tangents are drawn to the circle.  
  
 
|-
 
|-
−
|07.16
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|07:16
 
|Tangents meet at two points on the circle.
 
|Tangents meet at two points on the circle.
  
 
|-
 
|-
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|07.20
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|07:20
 
|Click on the "Intersect two objects" tool Mark points of contact as 'E' and 'F'.  
 
|Click on the "Intersect two objects" tool Mark points of contact as 'E' and 'F'.  
  
 
|-
 
|-
−
|07.28
+
|07:28
 
|Let's draw a triangle.Click on the "Polygon" tool.  
 
|Let's draw a triangle.Click on the "Polygon" tool.  
  
 
|-
 
|-
−
|07.31
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|07:31
 
|Click on the points 'B' 'C' 'F' and 'B' once again to complete the figure.  
 
|Click on the points 'B' 'C' 'F' and 'B' once again to complete the figure.  
  
 
|-
 
|-
−
|07.41
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|07:41
 
|In the figure 'BF' is the chord to the circle 'c'.
 
|In the figure 'BF' is the chord to the circle 'c'.
  
 
|-
 
|-
−
|07.45
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|07:45
 
|'∠FCB' is the inscribed angle by the chord to the circle 'c'.  
 
|'∠FCB' is the inscribed angle by the chord to the circle 'c'.  
  
 
|-
 
|-
−
|07.53
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|07:53
 
|'∠DFB' is angle between  tangent and chord to the circle 'c'.
 
|'∠DFB' is angle between  tangent and chord to the circle 'c'.
  
 
|-
 
|-
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|08.01
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|08:01
 
|Lets Measure the angles, Click on the "Angle" tool, click on the points D' 'F' 'B' and  'F' 'C' 'B'.
 
|Lets Measure the angles, Click on the "Angle" tool, click on the points D' 'F' 'B' and  'F' 'C' 'B'.
  
 
|-
 
|-
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|08.14
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|08:14
 
|Notice that  '∠DFB' = '∠FCB'. Let us move the point 'D' & 'C' that tangents and chords move along with point 'D'.
 
|Notice that  '∠DFB' = '∠FCB'. Let us move the point 'D' & 'C' that tangents and chords move along with point 'D'.
  
 
|-
 
|-
−
|08.31
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|08:31
 
|Let us save the file now.Click on “File”>> "Save As"  
 
|Let us save the file now.Click on “File”>> "Save As"  
  
 
|-
 
|-
−
|08.36
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|08:36
 
|I will type the file name as "Tangent-angle" Click on "Save" With this we come to the end of this tutorial.  
 
|I will type the file name as "Tangent-angle" Click on "Save" With this we come to the end of this tutorial.  
  
 
|-
 
|-
−
|08.50
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|08:50
 
|Let's summarize,In this tutorial, we have learnt to verify that;  
 
|Let's summarize,In this tutorial, we have learnt to verify that;  
 
 
 
|-
 
|-
−
|08.57
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|08:57
 
|"Two tangents drawn from an external point are equal"  
 
|"Two tangents drawn from an external point are equal"  
  
 
|-
 
|-
−
|09.01
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|09:01
 
|"Angle between a tangent and radius of a circle is 90^0"  
 
|"Angle between a tangent and radius of a circle is 90^0"  
  
 
|-
 
|-
−
|09.07
+
|09:07
 
|"Angle between tangent and a chord is equal to inscribed angle subtended by the chord "  
 
|"Angle between tangent and a chord is equal to inscribed angle subtended by the chord "  
  
 
|-
 
|-
−
|09.14
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|09:14
 
|As an assignment I would like you to verify:  
 
|As an assignment I would like you to verify:  
  
 
|-
 
|-
−
|09.17
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|09:17
 
|"Angle between tangents drawn to an circle, is supplementary to the angle subtended by the line-segment joining the points of contact at the centre".  
 
|"Angle between tangents drawn to an circle, is supplementary to the angle subtended by the line-segment joining the points of contact at the centre".  
  
 
|-
 
|-
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|09.30
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|09:30
 
|To verify ,Draw a circle.
 
|To verify ,Draw a circle.
  
Line 307: Line 307:
  
 
|-
 
|-
−
|09.37
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|09:37
 
|Mark points of contact of the tangents. Join centre of circle to  points of contact.
 
|Mark points of contact of the tangents. Join centre of circle to  points of contact.
  
 
|-
 
|-
−
|09.44
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|09:44
 
|Measure angle at the centre, Measure angle between the tangents.  
 
|Measure angle at the centre, Measure angle between the tangents.  
  
 
|-
 
|-
−
|09.49
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|09:49
 
|What is the sum of about two angles? Join centre and external point.
 
|What is the sum of about two angles? Join centre and external point.
  
 
|-
 
|-
−
|09.55
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|09:55
 
|Does the line-segment bisect the angle at the centre? Hint - Use Angle Bisector tool.
 
|Does the line-segment bisect the angle at the centre? Hint - Use Angle Bisector tool.
  
 
|-
 
|-
−
|10.05
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|10:05
 
|The output  should look like this,
 
|The output  should look like this,
  
  
 
|-
 
|-
−
|10.08
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|10:08
 
|Sum of the angles is 180^0. The line segments bisects the angle.
 
|Sum of the angles is 180^0. The line segments bisects the angle.
  
  
 
|-
 
|-
−
|10.16
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|10:16
 
|Watch the video available at this url http://spoken-tutorial.org/
 
|Watch the video available at this url http://spoken-tutorial.org/
  
 
|-
 
|-
−
|10.19
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|10:19
 
|It summarises the Spoken Tutorial project. If you do not have good bandwidth,you can download and watch it  
 
|It summarises the Spoken Tutorial project. If you do not have good bandwidth,you can download and watch it  
  
 
|-
 
|-
−
|10.27
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|10:27
 
|The Spoken tutorial project team Conducts workshops using spoken tutorials.
 
|The Spoken tutorial project team Conducts workshops using spoken tutorials.
  
 
|-
 
|-
−
|10.32
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|10:32
 
|Gives certificates to those who pass an online test.
 
|Gives certificates to those who pass an online test.
  
 
|-
 
|-
−
|10.35
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|10:35
 
|For more details, please write to contact@spoken-tutorial.org.  
 
|For more details, please write to contact@spoken-tutorial.org.  
  
 
|-
 
|-
−
|10.42
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|10:42
 
|Spoken Tutorial Project is a part of  Talk to a Teacher project.  
 
|Spoken Tutorial Project is a part of  Talk to a Teacher project.  
  
 
|-
 
|-
−
|10.47
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|10:47
 
|It is supported by the National Mission on Education through ICT, MHRD, Government of India.
 
|It is supported by the National Mission on Education through ICT, MHRD, Government of India.
  
 
|-
 
|-
−
|10.54
+
|10:54
 
|More information on this Mission is available at this link http://spoken-tutorial.org/NMEICT-Intro ]
 
|More information on this Mission is available at this link http://spoken-tutorial.org/NMEICT-Intro ]
  
 
|-
 
|-
−
|10.59
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|10:59
 
|The script is contributed by Neeta Sawant from SNDT Mumbai.
 
|The script is contributed by Neeta Sawant from SNDT Mumbai.
  
 
|-
 
|-
−
|11.04
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|11:04
 
|This is Madhuri Ganpathi from IIT Bombay.
 
|This is Madhuri Ganpathi from IIT Bombay.
  
 
Thank you for joining
 
Thank you for joining

Revision as of 12:27, 9 July 2014

Time Narration
00:00 Hello Welcome to this tutorial on "Tangents to a circle in Geogebra".
00:06 At the end of this tutorial you will be able to Draw tangents to the circle,Understand the properties of Tangents.
00:17 We assume that you have the basic working knowledge of Geogebra.
00:22 If not,For relevant tutorials Please visit our website http://spoken-tutorial.org.
00:27 To record this tutorial, I am using Ubuntu Linux OS Version 11.10, Geogebra Version 3.2.47.0 .
00:41 We will use the following Geogebra tools 
   .Tangents,
   .Perpendicular Bisector,
   .Intersect two Objects,
   .Compass,
   .Polygon &
   .Circle with Center and Radius.
00:58 Let's open a new GeoGebra window.
01:01 Click on Dash home Media Applications. Under Type Choose Education and GeoGebra.
01:13 let's define tangents to a circle.
01:16 Tangent is a line that touches a circle at only one point.
01:22 The point of contact is called "point of tangency".
01:27 For this tutorial I will use "Grid" layout instead of "Axes",Right Click on the drawing pad.
01:35 uncheck "Axes" Select "Grid"
01:39 let us draw tangent to a circle.
01:42 First let us draw a circle.
01:45 Select “Circle with Center and Radius” tool from toolbar.
01:49 Mark a point 'A' on the drawing pad.
01:52 A dialogue box opens.
01:53 Let's type value '3' for radius,Click OK
01:58 A circle with centre 'A' and radius '3' cm is drawn.
02:04 Let's 'Move' the point 'A' & see that circle has same radius.
02:09 Click on the "New point" tool,Mark a point 'B' outside the circle.
02:15 "Select Segment between two points" tool.Join points 'A' and 'B'.A Segment AB is drawn.
02:25 Select "Perpendicular Bisector" tool, Click on the points 'A' & 'B'.Perpendicular bisector to segment 'AB' is drawn.
02:37 Segment 'AB' and Perpendicular bisector intersect at a point,Click on "Intersect two objects" tool.
02:44 Mark point of intersection as 'C' Let's Move point 'B',& 'C' how the perpendicular bisector and point 'C' move along with point 'B'.
02:59 How to verify 'C' is the midpoint of 'AB'?
03:02 Click on "Distance" tool. click on the points 'A' , 'C'. 'C' ,'B' Notice that 'AC' = 'CB' implies 'C' is the midpoint of 'AB'.


03:20 Select "Compass" tool from tool bar,C lick on the points 'C', 'B'. and 'C' once again... to complete the figure.
03:30 Two circles intersect at two points.


03:33 Click on the "Intersect two objects" tool Mark the points of intersection as 'D' and 'E'
03:42 Select "Segment between two points" tool.
03:45 Join points 'B', 'D' and 'B' , 'E' .


03:53 Segments 'BD' and 'BE' are tangents to the circle 'c'?
03:59 let's explore some of the properties of these Tangents to the circle.
04:05 Select "Segment between two points" tool.
04:08 Join points 'A', 'D' and 'A', 'E'.
04:14 In triangles 'ADB' and 'ABE' Segment 'AD'= segment 'AE' (radii of the circle 'c').

Let's see from the Algebra view that segment 'AD'=segment 'AE'.

04:34 '∠ADB'= '∠BEA' angle of the semicircle of circle 'D' Lets measure the "Angle".
04:48 Click on the "Angle" tool... Click on the points 'A', 'D', 'B' and 'B', 'E', 'A' angles are equal.
05:03 Segment 'AB' is common to both the triangles,therefore '△ADB' '≅' '△ABE' by "SAS rule of congruency"
05:20 It implies Tangents 'BD' and 'BE' are equal!
05:26 From the Algebra view, we can find that tangents 'BD' and 'BE' are equal
05:33 Please Notice that tangent is always at right angles to the radius of the circle where it touches,

Let us move the point 'B' & 'C' how the tangents move along with point 'B'.

05:50 Let us save the file now. Click on “File”>> "Save As"
05:54 I will type the file name as "Tangent-circle" Click on "Save"
06:08 Let's state a theorem
06:11 "Angle between tangent and chord at the point of tangency, is same as an inscribed angle subtended by the same chord". 
Angle DFB between tangents & chord= inscribed angle FCB of the chord BF.
06:34 Let's verify the theorem;
06:38 Let's open a new Geogebra window.click on “File” >> "New". Let's draw a circle.
06:48 Click on the "Circle with center through point" tool from tool bar . Mark a point 'A' as a centre and click again to get 'B'.
06:59 Select "New point" tool.Mark point'C' on the circumference and 'D' outside the circle.
07:06 Select "Tangents" tool from toolbar.click on the point 'D'... and on circumference.
07:14 Two Tangents are drawn to the circle.
07:16 Tangents meet at two points on the circle.
07:20 Click on the "Intersect two objects" tool Mark points of contact as 'E' and 'F'.
07:28 Let's draw a triangle.Click on the "Polygon" tool.
07:31 Click on the points 'B' 'C' 'F' and 'B' once again to complete the figure.
07:41 In the figure 'BF' is the chord to the circle 'c'.
07:45 '∠FCB' is the inscribed angle by the chord to the circle 'c'.
07:53 '∠DFB' is angle between tangent and chord to the circle 'c'.
08:01 Lets Measure the angles, Click on the "Angle" tool, click on the points D' 'F' 'B' and 'F' 'C' 'B'.
08:14 Notice that '∠DFB' = '∠FCB'. Let us move the point 'D' & 'C' that tangents and chords move along with point 'D'.
08:31 Let us save the file now.Click on “File”>> "Save As"
08:36 I will type the file name as "Tangent-angle" Click on "Save" With this we come to the end of this tutorial.
08:50 Let's summarize,In this tutorial, we have learnt to verify that;
08:57 "Two tangents drawn from an external point are equal"
09:01 "Angle between a tangent and radius of a circle is 90^0"
09:07 "Angle between tangent and a chord is equal to inscribed angle subtended by the chord "
09:14 As an assignment I would like you to verify:
09:17 "Angle between tangents drawn to an circle, is supplementary to the angle subtended by the line-segment joining the points of contact at the centre".
09:30 To verify ,Draw a circle.

Draw tangents from an external point.

09:37 Mark points of contact of the tangents. Join centre of circle to points of contact.
09:44 Measure angle at the centre, Measure angle between the tangents.
09:49 What is the sum of about two angles? Join centre and external point.
09:55 Does the line-segment bisect the angle at the centre? Hint - Use Angle Bisector tool.
10:05 The output should look like this,


10:08 Sum of the angles is 180^0. The line segments bisects the angle.


10:16 Watch the video available at this url http://spoken-tutorial.org/
10:19 It summarises the Spoken Tutorial project. If you do not have good bandwidth,you can download and watch it
10:27 The Spoken tutorial project team Conducts workshops using spoken tutorials.
10:32 Gives certificates to those who pass an online test.
10:35 For more details, please write to contact@spoken-tutorial.org.
10:42 Spoken Tutorial Project is a part of Talk to a Teacher project.
10:47 It is supported by the National Mission on Education through ICT, MHRD, Government of India.
10:54 More information on this Mission is available at this link http://spoken-tutorial.org/NMEICT-Intro ]
10:59 The script is contributed by Neeta Sawant from SNDT Mumbai.
11:04 This is Madhuri Ganpathi from IIT Bombay.

Thank you for joining

Contributors and Content Editors

Madhurig, Minal, PoojaMoolya, Pratik kamble, Sakinashaikh, Sandhya.np14, Sneha

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