Difference between revisions of "Geogebra/C3/Tangents-to-a-circle/English-timed"
From Script | Spoken-Tutorial
PoojaMoolya (Talk | contribs) |
|||
| Line 24: | Line 24: | ||
|- | |- | ||
|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. | + | |
|- | |- | ||
| Line 78: | Line 74: | ||
|- | |- | ||
|01:52 | |01:52 | ||
| − | |A dialogue box opens. | + | |A dialogue box opens. Let's type value '''3''' for radius, click '''OK'''. |
| − | + | ||
| − | + | ||
| − | + | ||
| − | + | ||
|- | |- | ||
Revision as of 17:13, 27 March 2017
| 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. 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
