Difference between revisions of "Geogebra/C3/Theorems-on-Chords-and-Arcs/English-timed"

Latest revision as of 14:48, 28 October 2020

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, 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 dialog box opens.
02:03	Let's type value 3 for radius.
02:06	Click OK. 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. 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

Difference between revisions of "Geogebra/C3/Theorems-on-Chords-and-Arcs/English-timed"

Latest revision as of 14:48, 28 October 2020

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@@ Line 3: / Line 3: @@
 |'''Narration'''
 |-
-||00.01
+||00:01
-||Hello,Welcome to this  tutorial on '''Theorems on Chords and Arcs in Geogebra'''
+||Hello. Welcome to this  tutorial on '''Theorems on Chords and Arcs in Geogebra'''.
 |-
-||00.08
+||00:08
-||At the end of this  tutorial,
+||At the end of this  tutorial, you will be able to  verify theorems on:
 |-
-||00.10
+||00:14
-||you will be able to  verify theorems on
+||Chords of circle.
- *Chords of circle.
-* Arcs of circle.
 |-
-||00.19
+||00:16
-||We assume that you have the basic working knowledge of Geogebra.
+|| Arcs of circle.
+|-
+||00:18
+||We assume that you have the basic working knowledge of '''Geogebra'''.
 |-
-||00.23
+||00:23
-||If not,For relevant tutorials, please visit our website http://spoken-tutorial.org
+||If not, for relevant tutorials, please visit our website:  http://spoken-tutorial.org
 |-
-|| 00.30
+|| 00:30
-||To record this tutorial I am using
+||To record this tutorial I am using:
 |-
-||00.33
+||00:32
-||Ubuntu Linux OS Version  11.10  Geogebra Version 3.2.47.0
+||'''Ubuntu Linux OS''' Version  11.10
+|-
+||00:36
+||'''Geogebra''' Version 3.2.47.0
 |-
-|00.43
+|00:42
-||We will use the following Geogebra tools
+||We will use the following '''Geogebra tools''':
 |-
-||00.47
+||00:47
-||* Circle with Center and Radius
+||Circle with Center and Radius
 |-
-||00.50
+||00:49
-||* Circular Sector with Center between Two Points
+||Circular Sector with Center between Two Points
 |-
-||00.53
+||00:53
-||* Circular Arc with Center between Two points
+||Circular Arc with Center between Two points
 |-
-||00.56
+||00:56
-||* Midpoint  and
+||Midpoint  and
-*Perpendicular line
 |-
-||01.00
+||00:58
+||Perpendicular line
+|-
+||01:00
 ||Let's open a new  GeoGebra window.
 |-
-||01.02
+||01:02
-||Click on  Dash  home  Media Apps.
+||Click on  '''Dash home''',  '''Media Apps'''.
 |-
-||01.07
+||01:06
-||Under Type Choose Education and  GeoGebra.
+||Under '''Type''', choose '''Education''' and  '''GeoGebra'''.
 |-
-||01.15
+||01:15
-||Let's state a  theorem
+||Let's state a  theorem:
 |-
-|| 01.18
+|| 01:17
-||   '''Perpendicular from center of  circle to a chord bisects the chord'''
+||"Perpendicular from center of  circle to a chord bisects the chord".
 |-
-||01.23
+||01:23
-||'''Perpendicular from center A   of a circle to chord BC bisects it'''
+||Perpendicular from the center '''A''' of a circle to chord '''BC''' bisects it.
 |-
-||01.32
+||01:32
-||Let's verify a theorem.
+||Let's verify the theorem.
-|-
-||01.37
-||For this tutorial  I will use 'Grid layout' instead of Axes
 |-
-||01.42
+||01:37
-||Right Click on the drawing pad
+||For this tutorial, I will use '''Grid''' layout instead of '''Axes'''.
 |-
-||01.44
+||01:42
-||In the 'Graphic view'
+||Right click on the drawing pad.
 |-
-||01.45
+||01:44
-||uncheck  'Axes' and
+||In the '''Graphic view''', uncheck '''Axes'''.
 |-
-||01.47
+||01:47
-||Select 'Grid'
+||Select '''Grid'''.
 |-
-||01.52
+||01:51
 ||Let's draw a circle.
 |-
-||01.54
+||01:54
-||Select the "Circle with Center and Radius"  tool from tool bar.
+||Select the '''Circle with Center and Radius'''  tool from tool bar.
 |-
-||01.58
+||01:58
-||Mark a point 'A'  on the drawing pad.
+||Mark a point '''A''' on the drawing pad.
 |-
-||02.01
+||02:01
-||A dialogue box   open
+||A dialog box opens.
 |-
-||02.03
+||02:03
-||Let's type value '3' for radius
+||Let's type value '''3''' for radius.
 |-
-||02.06
+||02:06
-||Click OK.
+||Click '''OK'''. A circle with center '''A''' and radius '''3cm''' is drawn.
-|-
-||02.07
-||A Circle with center 'A' and radius '3cm' is drawn
 |-
-||02.14
+||02:13
-||Let's Move the  point 'A' and  see the movement of the circle.
+||Let's move the  point '''A''' and  see the movement of the circle.
 |-
-||02.19
+||02:19
-||Select  “Segment between two points” tool.
+||Select  '''Segment between two points''' tool.
 |-
-||02.22
+||02:22
-||Mark points 'B'  and 'C'  on the circumference of the circle
+||Mark points '''B'''  and '''C'''  on the circumference of the circle.
 |-
-||02.27
+||02:27
-||A chord 'BC' is drawn.
+||A chord '''BC''' is drawn.
 |-
-||02.30
+||02:30
-||Let's draw a  perpendicular line to Chord 'BC'  which passes through point 'A'.
+||Let's draw a  perpendicular line to chord '''BC''' which passes through point '''A'''.
 |-
-||02.36
+||02:35
-||Click on  "Perpendicular line"  tool from tool bar
+||Click on  '''Perpendicular Line'''  tool from tool bar.
 |-
-||02.39
+||02:39
-||Click on  the chord  'BC', and point 'A'.
+||Click on  the chord  '''BC''' and point '''A'''.
 |-
-||02.45
+||02:44
-||Let's Move the  point 'B', and see how the perpendicular line moves along with point 'B'.
+||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
 |-
-||02.57
+||02:52
-||Click on “Intersect Two objects”  tool,
+||Perpendicular line and chord '''BC''' intersect at a point.
 |-
-||02.59
+||02:56
-||Mark the point of intersection as 'D'.
+||Click on '''Intersect Two Objects'''  tool.
 |-
-||03.04
+||02:58
-||Let's verify whether D is the mid point of chord BC
+||Mark the point of intersection as '''D'''.
 |-
-||03.09
+||03:03
-||Click on the "Distance"  tool...
+||Let's verify whether '''D''' is the mid point of chord '''BC'''.
 |-
-||03.12
+||03:08
-||Click on the points ,'B'  'D' ...'D'  'C' ...
+||Click on the '''Distance''' tool.
 |-
-||03.19
+||03:11
-||Notice that distances 'BD' and 'DC' are equal.
+||Click on the points '''B''', '''D''' ...'''D''', '''C''' .
 |-
-||03.24
+||03:19
-||It implies 'D' is midpoint of  chord 'BC'
+||Notice that distances '''BD''' and '''DC''' are equal.
 |-
-||03.29
+||03:24
-||Let's measure the angle 'CDA'
+||It implies '''D''' is midpoint of  chord '''BC'''
+|-
+||03:29
+||Let's measure the angle '''CDA'''.
 |-
-||03.33
+||03:33
-||Click on Angle tool  ...
+||Click on '''Angle''' tool.
 |-
-||03.36
+||03:35
-||Click on the points    'C','D', 'A'
+||Click on the points '''C''', '''D''', '''A''',
 |-
-||03.42
+||03:42
-||  angle 'CDA' is '90^0'.
+||angle '''CDA''' is '90' degrees.
 |-
-||03.46
+||03:46
-|| TheTheorem is verified.
+|| The theorem is verified.
 |-
-||03.50
+||03:50
-||Let's Move the point  'C'
+||Let's move the point  '''C'''  and see how the distances move along with point 'C'.
 |-
-||03.52
+||04:03
-||and see how the distances move along with point 'C'
+||Let us save the file now.
 |-
-||04.03
+||04:05
-||Let us save the file now
+||Click on  '''File''' >> '''Save As'''.
 |-
-||04.05
+||04:08
-||Click on  “File”>>  "Save As"
+||I will type the file name as '''circle-chord'''.
 |-
-||04.08
+||04:12
-||I will type the file name as "circle-chord" click on “Save”
+||'''circle-chord'''.
 |-
-||04.21
+||04:16
+|| Click on '''Save'''.
+|-
+||04:21
 ||Let us move on to the next theorem.
 |-
-||04.28
+||04:28
-||'''Inscribed angles subtended by the same arc are equal.'''
+||"Inscribed angles subtended by the same arc are equal".
 |-
-||04.34
+||04:34
-||'''Inscribed angles BDC and BEC subtended by the same arc BC are equal'''
+||Inscribed angles '''BDC''' and '''BEC''' subtended by the same arc '''BC''' are equal.
 |-
-||04.44
+||04:44
 ||Let's verify the theorem.
 |-
-||04.54
+||04:48
-||Let'sOpen a new Geogebra window,
+||Let's open a new Geogebra window.
 |-
-||04.51
+||04:51
-||Click on “File” >> "New"
+||Click on '''File''' >> '''New'''.
 |-
-||04.55
+||04:55
-||Let's draw a  ''circle''
+||Let's draw a circle.
 |-
-||04.57
+||04:57
-||Click on " the Circle with Center through point tool from toolbar"
+||Click on '''Circle with Center through Point''' tool, from toolbar.
 |-
-||05.01
+||05:01
-||Mark a point A' as centre
+||Mark a point '''A''' as centre,
 |-
-||05.04
+||05:04
-|| and click again to get point 'B' and 'C'  on the circumference
+|| and click again to get point '''B'''.
 |-
-||05.09
+||05:10
-||Let's draw an arc 'BC'
+||Let's draw an arc '''BC'''.
 |-
-||05.13
+||05:13
-||Click on "Circular Arc with Center between Two points"
+||Click on '''Circular Arc with Center between Two Points'''.
 |-
-||05.18
+||05:17
-||Click on the point 'A'B' and 'C'  on the circumference
+||Click on the points '''A''', '''B''' and '''C''' on the circumference.
+|-
+||05:24
+||An arc '''BC''' is drawn.
-|-
-||05.24
-||An Arc 'BC' is drawn
 |-
-||05.27
+||05:26
-||Let's change the  properties of arc 'BC'
+||Let's change the  properties of arc '''BC'''.
 |-
-||05.30
+||05:30
-||In the "Algebra View"
+||In the '''Algebra View''',
 |-
-||05.32
+||05:32
-||Right click on the object 'd'
+||right click on the object '''d'''.
 |-
-||05.35
+||05:35
-||Select  "Object Properties"
+||Select  '''Object Properties'''.
 |-
-||05.38
+||05:37
-||Select '' color'' as ''green'' click on close.
+||Select Color as '''green''',  click on '''Close.'''
 |-
-||05.46
+||05:46
-|| Click on new point tool, mark points  'D' and 'E' on the circumference of the circle.
+|| Click on '''New Point''' tool, mark points  '''D''' and '''E''' on the circumference of the circle.
 |-
-||05.56
+||05:56
-||let's subtend two angles from arc BC to points  'D' And 'E'.
+||Let's subtend two angles from arc BC to points  '''D''' and '''E'''.
 |-
-||06.04
+||06:03
-||Click on "Polygon" tool,
+||Click on '''Polygon''' tool,
 |-
-||06.05
+||06:05
-||click on the  points  'E', 'B', 'D', 'C' and 'E'  again to complete the figure.
+||click on the  points  '''E''', '''B''', '''D''', '''C''' and '''E'''  again, to complete the figure.
 |-
-||06.18
+||06:18
-||Let's measure the angles  'BDC'  and 'BEC'
+||Let's measure the angles  '''BDC'''  and '''BEC'''.
 |-
-||06.27
+||06:26
-||Click on the "Angle" tool,
+||Click on the '''Angle''' tool,
 |-
-||06.29
+||06:28
-||Click  on points  'B', 'D', 'C' and     'B', 'E', 'C'
+||Click  on points  '''B''', '''D''', '''C''' and     '''B''', '''E''', '''C'''.
 |-
-||06.40
+||06:40
-||We can see that the angles  'BDC'  and  'BEC' are equal.
+||We can see that the angles  '''BDC'''  and  '''BEC''' are equal.
 |-
-||06.52
+||06:51
-||Let's state a next theorem
+||Let's state a next theorem.
 |-
-||06.55
+||06:55
-||'''Angle subtended by an arc at the center, is twice the  inscribed angles subtended by the same arc '''
+||"Angle subtended by an arc at the center is twice the inscribed angles subtended by the same arc".
 |-
-||07.06
+||07:06
-||'''Angle BAC subtended by arc BC at A is twice the inscribed angles BEC and BDC subtended by the same arc '''
+||Angle '''BAC''' subtended by arc '''BC''' at '''A''' is twice the inscribed angles '''BEC''' and '''BDC''', subtended by the same  arc.
 |-
-||07.22
+||07:22
-||Let's verify the theorem
+||Let's verify the theorem.
 |-
-||07.26
+||07:26
-||Let's draw a sector 'ABC'
+||Let's draw a sector '''ABC'''.
 |-
-||07.30
+||07:30
-||Click on the  "Circular Sector with Center between Two Points" tool.
+||Click on the '''Circular Sector with Center between Two Points''' tool.
 |-
-||07.35
+||07:35
-||click on the  points 'A',  'B', 'C'
+||Click on the  points '''A''', '''B''', '''C'''.
 |-
-||07.45
+||07:45
-||Let's change the color of   sector 'ABC'.
+||Let's change the color of sector '''ABC'''.
 |-
-||07.48
+||07:48
-||Right click on sector 'ABC'
+||Right click on sector '''ABC'''.
 |-
-||07.51
+||07:51
-||Select "Object Properties".
+||Select '''Object Properties'''.
 |-
-||07.54
+||07:54
-||Select Color as “Green”. Click on "Close".
+||Select Color as '''Green'''. Click on '''Close'''.
 |-
-||08.00
+||08:00
-||Let's the measure angle 'BAC'
+||Let's measure the angle '''BAC'''.
 |-
-||08.04
+||08:04
-||Click on  the "Angle" tool , Click on the points 'B', 'A', 'C'
+||Click on  the '''Angle''' tool , click on the points '''B''', '''A''', '''C'''.
 |-
-||08.15
+||08:15
-||Angle  'BAC' is twice the angles  'BEC' and 'BDC'
+||Angle  '''BAC''' is twice the angles  '''BEC''' and '''BDC'''.
 |-
-||08.28
+||08:28
-||Let's move the point 'C'
+||Let's move the point '''C'''.
 |-
-||08.32
+||08:32
-||Notice that   angle  'BAC' is always twice the angles  'BEC' and 'BDC'
+||Notice that   angle  '''BAC''' is always twice the angles  '''BEC''' and '''BDC'''.
 |-
-||08.41
+||08:41
-||hence theorems  are verified
+||Hence the theorems  are verified.
 |-
-||08.45
+||08:45
-||With this we come to the end of the tutorial
+||With this, we come to the end of this tutorial.
 |-
-||08.48
+||08:48
-||let's summarize
+||Let's summarize.
 |-
-||08.53
+||08:53
 ||In this tutorial, we have learnt to verify that:
 |-
-||08.57
+||08:57
-||*  Perpendicular   from center to a  chord bisects it
+||Perpendicular  from center to a  chord bisects it
 |-
-||09.00
+||09:00
-||*  Inscribed angles subtended by the same  arc  are equal
+||Inscribed angles subtended by the same  arc  are equal
 |-
-||09.06
+||09:06
-||* the Central angle of a circle is twice any inscribed angle subtended by the same arc
+||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
+|| 09:15
-||Equal chords of a circle are equidistant from center.
+|| As an assignment,  I would like you to verify
 |-
-||09.24
+||09:19
-||Draw a circle.
+||Equal chords of a circle are equidistant from center.
 |-
-||09.26
+||09:24
-||Select Segment with Given length from point tool
+||Draw a circle. Select Segment with given length from point tool.
 |-
-||09.29
+||09:29
 ||Use it to draw two chords of equal size.
 |-
-||09.33
+||09:33
 ||Draw perpendicular lines from center  to chords.
 |-
-||09.37
+||09:37
 ||Mark points of intersection.
 |-
-||09.40
+||09:40
 ||Measure  perpendicular distances.
 |-
-||09.44
+||09:44
-||Assignment  out put should look like this
+||Assignment  output should look like this.
 |-
-||09.48
+||09:48
-||Watch the video available at this url  http://spoken-tutorial.org/What is a Spoken Tutorial
+||Watch the video available at this url:  http://spoken-tutorial.org/What is a Spoken Tutorial
 |-
-||09.51
+||09:51
-||It summarises the Spoken Tutorial project
+||It summarizes the Spoken Tutorial project.
 |-
-||09.53
+||09:53
-||If you do not have good bandwidth, you can download and watch it
+||If you do not have good bandwidth, you can download and watch it.
 |-
-||09.58
+||09:58
 ||The Spoken Tutorial Project Team :
 |-
-||10.00
+||10:00
-||Conducts workshops using spoken tutorials
+||Conducts workshops using spoken tutorials.
 |-
-||10.03
+||10:03
-||Gives certificates to those who pass an online test
+||Gives certificates to those who pass an online test.
 |-
-||10.07
+||10:06
-||For more details, please write to contact@spoken-tutorial.org
+||For more details, please write to contact@spoken-tutorial.org.
 |-
-||10.14
+||10:14
-||Spoken Tutorial Project is a part  of the Talk to a Teacher project
+||Spoken Tutorial Project is a part  of the Talk to a Teacher project.
 |-
-||10.18
+||10:18
-||It is supported by the National Mission on Education through ICT, MHRD, Government of India
+||It is supported by the National Mission on Education through ICT, MHRD, Government of India.
 |-
-||10.25
+||10:25
-||More information on this Mission is available at http://spoken-tutorial.org/NMEICT-Intro ]
+||More information on this mission is available at this link.
 |-
-||10.29
+||10:29
-||This is Madhuri Ganapathi from IIT Bombay signing off .Thank you  for joining
+||This is Madhuri Ganapathi from IIT Bombay, signing off .Thank you  for joining.