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

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Revision as of 11:34, 24 February 2015

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, 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. 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 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 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 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 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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