Difference between revisions of "Geogebra/C3/Tangents-to-a-circle/English-timed"
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− | |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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Revision as of 13:02, 18 April 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 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 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 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