Difference between revisions of "Geogebra/C3/Tangents-to-a-circle/English-timed"
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|Sum of the angles is 180^0. The line segments bisects the angle. | |Sum of the angles is 180^0. The line segments bisects the angle. | ||
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Revision as of 16:57, 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
