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.
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