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".  
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|Hello Welcome to this tutorial on '''Tangents to a circle in Geogebra'''.  
  
 
|-
 
|-
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|-
 
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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
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|uncheck "Axes" Select "Grid"
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|uncheck '''Axes''' Select '''Grid'''
  
 
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|-
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|-
 
|-
 
|01:53
 
|01:53
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|Let's type value '3' for radius,Click OK
+
|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
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|Let's 'Move' the point 'A' & see that circle has same radius.
+
|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.
+
|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.
+
| "Select Segment between two points" tool.Join points '''A''' and '''B'''.A Segment AB is drawn.
  
 
|-
 
|-
 
|02:25
 
|02:25
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|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
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|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'''.  
  
 
|-
 
|-
 
|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
−
|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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|-
 
|-
 
|03:33
 
|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
−
|Select "Segment between two points" tool.
+
|Select '''Segment between two points''' tool.
  
 
|-
 
|-
 
|03:45
 
|03:45
−
|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'''?  
  
 
|-
 
|-
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|-
 
|-
 
|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''' Lets 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
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|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  
  
 
|-
 
|-
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|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' & 'C' 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
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|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
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|I will type the file name as "Tangent-circle" Click on "Save"
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|I will type the file name as '''Tangent-circle''' Click on '''Save'''
  
 
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|-
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|06:11
 
|06:11
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|"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.
  
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|-
 
|-
 
|06:38
 
|06:38
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|Let's open a new Geogebra window.click on “File” >> "New". Let's draw a circle.
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|Let's open a new Geogebra window.click on '''File''' >> '''New'''. Let's draw a circle.
  
 
|-
 
|-
 
|06:48
 
|06:48
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|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
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|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
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|Select "Tangents" tool from toolbar.click on the point 'D'... and on circumference.  
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|Select '''Tangents''' tool from toolbar.click on the point '''D'''... and on circumference.  
  
 
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|07:20
 
|07:20
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|Click on the "Intersect two objects" tool Mark points of contact as 'E' and 'F'.  
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|Click on the '''Intersect two objects''' tool Mark points of contact as '''E''' and '''F'''.  
  
 
|-
 
|-
 
|07:28
 
|07:28
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|Let's draw a triangle.Click on the "Polygon" tool.  
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|Let's draw a triangle.Click on the '''Polygon''' tool.  
  
 
|-
 
|-
 
|07:31
 
|07:31
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|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
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|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
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|'∠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'.
+
|'''∠DFB''' is angle between  tangent and chord to the circle '''c'''.
  
 
|-
 
|-
 
|08:01
 
|08:01
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|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
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|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
 
|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
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|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.  
  
 
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|-
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|08:57
 
|08:57
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|"Two tangents drawn from an external point are equal"
+
|'''Two tangents drawn from an external point are equal'''
  
 
|-
 
|-
 
|09:01
 
|09:01
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|"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
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|"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'''
  
 
|-
 
|-
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|-
 
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|09:17
 
|09:17
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|"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'''.  
  
 
|-
 
|-

Revision as of 16:53, 3 September 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 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,& 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 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 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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