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

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|00:00
 
|00:00
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|Hello Welcome to this tutorial on "Tangents to a circle in Geogebra".  
+
|Hello. Welcome to this tutorial on '''Tangents to a circle in Geogebra'''.  
  
 
|-
 
|-
 
|00:06
 
|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.
  
 
|-
 
|-
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|-
 
|-
 
|00:22
 
|00:22
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|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
 
|00:41
−
|We will use the following Geogebra tools
+
|We will use the following Geogebra tools: Tangents, Perpendicular Bisector
−
    .Tangents,
+
 
−
    .Perpendicular Bisector,
+
Intersect two Objects, Compass, Polygon & Circle with Center and Radius.
−
    .Intersect two Objects,
+
−
    .Compass,
+
−
    .Polygon &
+
−
    .Circle with Center and Radius.
+
  
 
|-
 
|-
 
|00:58
 
|00:58
−
|Let's open a new GeoGebra window.
+
|Let's open a new Geogebra window.
  
 
|-
 
|-
 
|01:01
 
|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
 
|01:13
−
|let's define tangents to a circle.
+
|Let's define tangents to a circle.
  
 
|-
 
|-
 
|01:16
 
|01:16
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|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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|-
 
|-
 
|01:27
 
|01:27
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|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.
  
 
|-
 
|-
 
|01:35
 
|01:35
−
|uncheck "Axes" Select "Grid"
+
|Uncheck '''Axes''', select '''Grid'''.
  
 
|-
 
|-
 
|01:39
 
|01:39
−
| let us draw tangent to a circle.
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| Let us draw tangent to a circle.
  
 
|-
 
|-
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|-
 
|-
 
|01:45
 
|01:45
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|Select “Circle with Center and Radius” tool from toolbar.
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|Select '''Circle with Center and Radius''' tool from toolbar.
  
 
|-
 
|-
 
|01:49
 
|01:49
−
|Mark a point 'A' on the drawing pad.
+
|Mark a point '''A''' on the drawing pad.
  
 
|-
 
|-
 
|01:52
 
|01:52
−
|A dialogue box opens.  
+
|A dialog box opens. Let's type value '''3''' for radius, click '''OK'''.
−
 
+
−
|-
+
−
|01:53
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−
|Let's type value '3' for radius,Click OK
+
  
 
|-
 
|-
 
|01:58
 
|01:58
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|A circle with centre 'A' and radius '3' cm is drawn.  
+
|A circle with centre '''A''' and radius '''3''' cm is drawn.  
  
 
|-
 
|-
 
|02:04
 
|02:04
−
|Let's 'Move' the point 'A' & see that circle has same radius.
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|Let's move the point '''A''' & see that circle has same radius.
  
 
|-
 
|-
 
|02:09
 
|02:09
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|Click on the "New point" tool,Mark a point 'B' outside the circle.
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|Click on the '''New Point'''tool. Mark a point '''B''' outside the circle.
  
 
|-
 
|-
 
|02:15
 
|02:15
−
| "Select Segment between two points" tool.Join points 'A' and 'B'.A Segment AB is drawn.
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|Select '''Segment between Two Points''' tool. Join points '''A''' and '''B'''. A segment '''AB''' is drawn.
  
 
|-
 
|-
 
|02:25
 
|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.
  
 
|-
 
|-
 
|02:37
 
|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.  
  
 
|-
 
|-
 
|02:44
 
|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''' & see how the perpendicular bisector and point '''C''' move along with point '''B'''.  
  
 
|-
 
|-
 
|02:59
 
|02:59
−
|How to verify 'C' is the midpoint of 'AB'?
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|How to verify '''C''' is the midpoint of '''AB'''?
  
 
|-
 
|-
 
|03:02
 
|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'''.
−
 
+
  
 
|-
 
|-
 
|03:20
 
|03:20
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|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, click on the points '''C''', '''B''' and '''C''' once again... to complete the figure.  
  
 
|-
 
|-
 
|03:30
 
|03:30
 
|Two circles intersect at two points.
 
|Two circles intersect at two points.
−
 
  
 
|-
 
|-
 
|03:33
 
|03:33
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|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'''.
  
 
|-
 
|-
 
|03:42
 
|03:42
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|Select "Segment between two points" tool.
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|Select '''Segment between Two Points''' tool.
  
 
|-
 
|-
 
|03:45
 
|03:45
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|Join points 'B', 'D'  and 'B' , 'E' .  
+
|Join points '''B''', '''D'''  and '''B''' , '''E''' .  
−
 
+
  
 
|-
 
|-
 
|03:53
 
|03:53
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|Segments 'BD' and 'BE' are tangents to the circle 'c'?
+
|Segments '''BD''' and '''BE''' are tangents to the circle '''c'''.
  
 
|-
 
|-
 
|03:59
 
|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.
  
 
|-
 
|-
 
|04:05
 
|04:05
−
|Select "Segment between two points" tool.
+
|Select '''Segment between Two Points''' tool.
  
 
|-
 
|-
 
|04:08
 
|04:08
−
|Join points 'A', 'D' and 'A', 'E'.
+
|Join points '''A''', '''D''' and '''A''', '''E'''.
  
 
|-
 
|-
 
|04:14
 
|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').  
  
−
Let's see from the Algebra view that segment 'AD'=segment 'AE'.
+
Let's see from the '''Algebra View''' that segment '''AD'''= segment '''AE'''.
  
 
|-
 
|-
 
|04:34
 
|04:34
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|'∠ADB'= '∠BEA' angle of the semicircle of circle 'D' Lets measure the "Angle".
+
|'''∠ADB'''= '''∠BEA''', angle of the semicircle of circle '''d'''. Let's measure the angle.
  
 
|-
 
|-
 
|04:48
 
|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.
  
 
|-
 
|-
 
|05:03
 
|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'''.
  
 
|-
 
|-
 
|05:20
 
|05:20
−
|It implies Tangents 'BD' and 'BE' are equal!
+
|It implies:  tangents '''BD''' and '''BE''' are equal!
 
   
 
   
 
|-
 
|-
 
|05:26
 
|05:26
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|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.
  
 
|-
 
|-
 
|05:33
 
|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.
−
+
Let us move the point '''B''' & see how the tangents move along with point '''B'''.
−
Let us move the point 'B' & 'C' how the tangents move along with point 'B'.
+
  
 
|-
 
|-
 
|05:50
 
|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
 
|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  
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|Let's state a theorem.
 
   
 
   
 
|-
 
|-
 
|06:11
 
|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 tangent & chord = inscribed angle FCB of the chord BF.
  
 
|-
 
|-
 
|06:34
 
|06:34
−
|Let's verify the theorem;
+
|Let's verify the theorem. 
  
 
|-
 
|-
 
|06:38
 
|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
 
|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
 
|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.  
  
 
|-
 
|-
 
|07:14
 
|07:14
−
|Two Tangents are drawn to the circle.  
+
|Two tangents are drawn to the circle.  
  
 
|-
 
|-
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|-
 
|-
 
|07:20
 
|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
 
|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
 
|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
 
|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
 
|07:53
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|'∠DFB' is angle between  tangent and chord to the circle 'c'.
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|'''∠DFB''' is the angle between  tangent and chord to the circle '''c'''.
  
 
|-
 
|-
 
|08:01
 
|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'''.
  
 
|-
 
|-
 
|08:14
 
|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''' & see that tangents and chords move along with point 'D'.
  
 
|-
 
|-
 
|08:31
 
|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
 
|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
 
|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
 
|08:57
−
|"Two tangents drawn from an external point are equal"
+
|Two tangents drawn from an external point are equal  
  
 
|-
 
|-
 
|09:01
 
|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
 
|09:14
−
|As an assignment I would like you to verify:  
+
|As an assignment, I would like you to verify:  
  
 
|-
 
|-
 
|09:17
 
|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 a circle, is supplementary to the angle subtended by the line segments joining the points of contact at the centre".  
  
 
|-
 
|-
 
|09:30
 
|09:30
−
|To verify ,Draw a circle.
+
|To verify: Draw a circle. Draw tangents from an external point.
−
 
+
−
Draw tangents from an external point.
+
  
 
|-
 
|-
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|-
 
|09:44
 
|09:44
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|Measure angle at the centre, Measure angle between the tangents.  
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|Measure angle at the centre, measure angle between the tangents.  
  
 
|-
 
|-
 
|09:49
 
|09:49
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|What is the sum of about two angles? Join centre and external point.
+
|What is the sum of above two angles? Join centre and external point.
  
 
|-
 
|-
 
|09:55
 
|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
 
|10:05
−
|The output should look like this,
+
|The output should look like this.
−
 
+
  
 
|-
 
|-
 
|10:08
 
|10:08
−
|Sum of the angles is 180^0. The line segments bisects the angle.
+
|Sum of the angles is 180^0. The line segment bisects the angle.
−
 
+
  
 
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|-
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|10:19
 
|10:19
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|It summarises the Spoken Tutorial project. If you do not have good bandwidth,you can download and watch it  
+
|It summarizes the Spoken Tutorial project. If you do not have good bandwidth, you can download and watch it.
  
 
|-
 
|-
 
|10:27
 
|10:27
−
|The Spoken tutorial project team Conducts workshops using spoken tutorials.
+
|The Spoken tutorial project team: Conducts workshops using spoken tutorials.
  
 
|-
 
|-
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|-
 
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|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].
  
 
|-
 
|-
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|This is Madhuri Ganpathi from IIT Bombay.
 
|This is Madhuri Ganpathi from IIT Bombay.
  
−
Thank you for joining
+
Thank you for joining.

Latest revision as of 14:39, 28 October 2020

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 dialog box opens. 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 Pointtool. 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 & see 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, click 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. Let's 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 & see 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 tangent & 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 pointC 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 the 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 & see 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 a circle, is supplementary to the angle subtended by the line segments 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 above 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 segment bisects the angle.
10:16 Watch the video available at this url http://spoken-tutorial.org/
10:19 It summarizes 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 [1].
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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