Geogebra/C3/Tangents-to-a-circle/English-timed

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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/
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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