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

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 dialog 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