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 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 point" tool,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 point'C' 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.
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10:47	It is supported by the National Mission on Education through ICT, MHRD, Government of India.
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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