Geogebra/C3/Theorems-on-Chords-and-Arcs/English-timed

Time	Narration
00:01	Hello. Welcome to this tutorial on Theorems on Chords and Arcs in Geogebra.
00:08	At the end of this tutorial,
00:09	you will be able to verify theorems on:
00:14	Chords of circle.
00:16	Arcs of circle.
00:18	We assume that you have the basic working knowledge of Geogebra.
00:23	If not, for relevant tutorials, please visit our website: http://spoken-tutorial.org
00:30	To record this tutorial I am using:
00:32	Ubuntu Linux OS Version 11.10
00:36	Geogebra Version 3.2.47.0
00:42	We will use the following Geogebra tools:
00:47	* Circle with Center and Radius
00:49	* Circular Sector with Center between Two Points
00:53	* Circular Arc with Center between Two points
00:56	* Midpoint and
00:58	* Perpendicular line
01:00	Let's open a new GeoGebra window.
01:02	Click on Dash home, Media Apps.
01:06	Under Type, choose Education and GeoGebra.
01:15	Let's state a theorem:
01:17	"Perpendicular from center of circle to a chord bisects the chord".
01:23	Perpendicular from the center A of a circle to chord BC bisects it.
01:32	Let's verify the theorem.
01:37	For this tutorial, I will use Grid layout instead of Axes.
01:42	Right click on the drawing pad.
01:44	In the Graphic view, uncheck Axes.
01:47	Select Grid.
01:51	Let's draw a circle.
01:54	Select the Circle with Center and Radius tool from tool bar.
01:58	Mark a point A on the drawing pad.
02:01	A dialogue box opens.
02:03	Let's type value 3 for radius.
02:06	Click OK.
02:07	A circle with center A and radius 3cm is drawn.
02:13	Let's move the point A and see the movement of the circle.
02:19	Select Segment between two points tool.
02:22	Mark points B and C on the circumference of the circle.
02:27	A chord BC is drawn.
02:30	Let's draw a perpendicular line to chord BC which passes through point A.
02:35	Click on Perpendicular Line tool from tool bar.
02:39	Click on the chord BC and point A.
02:44	Let's move the point B and see how the perpendicular line moves along with point 'B'.
02:52	Perpendicular line and chord BC intersect at a point.
02:56	Click on Intersect Two objects tool.
02:58	Mark the point of intersection as D.
03:03	Let's verify whether D is the mid point of chord BC.
03:08	Click on the Distance tool.
03:11	Click on the points B, D ...D, C .
03:19	Notice that distances BD and DC are equal.
03:24	It implies D is midpoint of chord BC
03:29	Let's measure the angle CDA.
03:33	Click on Angle tool.
03:35	Click on the points C, D, A,
03:42	angle CDA is '90' degrees.
03:46	The theorem is verified.
03:50	Let's move the point C and see how the distances move along with point 'C'.
04:03	Let us save the file now.
04:05	Click on File >> Save As.
04:08	I will type the file name as circle-chord.
04:12	circle-chord.
04:16	Click on Save.
04:21	Let us move on to the next theorem.
04:28	"Inscribed angles subtended by the same arc are equal".
04:34	Inscribed angles BDC and BEC subtended by the same arc BC are equal.
04:44	Let's verify the theorem.
04:48	Let's open a new Geogebra window.
04:51	Click on File >> New.
04:55	Let's draw a circle.
04:57	Click on Circle with Center through Point tool, from toolbar.
05:01	Mark a point A as centre,
05:04	and click again to get point B.
05:10	Let's draw an arc BC.
05:13	Click on Circular Arc with Center between Two Points.
05:17	Click on the points A, B and C on the circumference.
05:24	An arc BC is drawn.
05:26	Let's change the properties of arc BC.
05:30	In the Algebra View,
05:32	right click on the object d.
05:35	Select Object Properties.
05:37	Select Color as green, click on Close.
05:46	Click on New Point tool, mark points D and E on the circumference of the circle.
05:56	Let's subtend two angles from arc BC to points D and E.
06:03	Click on Polygon tool,
06:05	click on the points E, B, D, C and E again, to complete the figure.
06:18	Let's measure the angles BDC and BEC.
06:26	Click on the Angle tool,
06:28	Click on points B, D, C and B, E, C.
06:40	We can see that the angles BDC and BEC are equal.
06:51	Let's state a next theorem.
06:55	"Angle subtended by an arc at the center is twice the inscribed angles subtended by the same arc".
07:06	Angle BAC subtended by arc BC at A is twice the inscribed angles BEC and BDC, subtended by the same arc.
07:22	Let's verify the theorem.
07:26	Let's draw a sector ABC.
07:30	Click on the Circular Sector with Center between Two Points tool.
07:35	Click on the points A, B, C.
07:45	Let's change the color of sector ABC.
07:48	Right click on sector ABC.
07:51	Select Object Properties.
07:54	Select Color as Green. Click on Close.
08:00	Let's measure the angle BAC.
08:04	Click on the Angle tool , click on the points B, A, C.
08:15	Angle BAC is twice the angles BEC and BDC.
08:28	Let's move the point C.
08:32	Notice that angle BAC is always twice the angles BEC and BDC.
08:41	Hence the theorems are verified.
08:45	With this we come to the end of this tutorial.
08:48	Let's summarize.
08:53	In this tutorial, we have learnt to verify that:
08:57	* Perpendicular from center to a chord bisects it
09:00	* Inscribed angles subtended by the same arc are equal
09:06	* the Central angle of a circle is twice any inscribed angle subtended by the same arc.
09:15	As an assignment, I would like you to verify
09:19	Equal chords of a circle are equidistant from center.
09:24	Draw a circle.
09:25	Select Segment with given length from point tool.
09:29	Use it to draw two chords of equal size.
09:33	Draw perpendicular lines from center to chords.
09:37	Mark points of intersection.
09:40	Measure perpendicular distances.
09:44	Assignment output should look like this.
09:48	Watch the video available at this url: http://spoken-tutorial.org/What is a Spoken Tutorial
09:51	It summarizes the Spoken Tutorial project.
09:53	If you do not have good bandwidth, you can download and watch it.
09:58	The Spoken Tutorial Project Team :
10:00	Conducts workshops using spoken tutorials.
10:03	Gives certificates to those who pass an online test.
10:06	For more details, please write to contact@spoken-tutorial.org.
10:14	Spoken Tutorial Project is a part of the Talk to a Teacher project.
10:18	It is supported by the National Mission on Education through ICT, MHRD, Government of India.
10:25	More information on this mission is available at this link.
10:29	This is Madhuri Ganapathi from IIT Bombay, signing off .Thank you for joining.

Contributors and Content Editors

Madhurig, PoojaMoolya, Pratik kamble, Sandhya.np14, Sneha