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

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|'''Narration'''   
 
|'''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,  
  
 
|-
 
|-
||00.10
+
||00:10
 
||you will be able to  verify theorems on  
 
||you will be able to  verify theorems on  
  
Line 17: Line 17:
 
* Arcs of circle.
 
* Arcs of circle.
 
|-
 
|-
||00.19
+
||00:19
 
||We assume that you have the basic working knowledge of Geogebra.   
 
||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
+
||00:33
 
||Ubuntu Linux OS Version  11.10  Geogebra Version 3.2.47.0  
 
||Ubuntu Linux OS Version  11.10  Geogebra Version 3.2.47.0  
 
|-
 
|-
|00.43
+
|00:43
 
||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
+
||00:50
 
||* 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  
 
*Perpendicular line  
 
|-
 
|-
||01.00
+
||01:00
 
||Let's open a new  GeoGebra window.
 
||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
+
||01:07
 
||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
+
|| 01:18
 
||  '''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 center A  of a circle to chord BC bisects it'''
  
 
|-
 
|-
||01.32
+
||01:32
 
||Let's verify a theorem.
 
||Let's verify a theorem.
 
|-
 
|-
||01.37
+
||01:37
 
||For this tutorial  I will use 'Grid layout' instead of Axes
 
||For this tutorial  I will use 'Grid layout' instead of Axes
  
 
|-
 
|-
||01.42
+
||01:42
 
||Right Click on the drawing pad  
 
||Right Click on the drawing pad  
  
 
|-
 
|-
||01.44
+
||01:44
 
||In the 'Graphic view'  
 
||In the 'Graphic view'  
  
 
|-
 
|-
||01.45
+
||01:45
 
||uncheck  'Axes' and
 
||uncheck  'Axes' and
  
 
|-
 
|-
||01.47
+
||01:47
 
||Select 'Grid'
 
||Select 'Grid'
 
|-
 
|-
||01.52
+
||01:52
 
||Let's draw a circle.
 
||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 dialogue box  open
 
|-
 
|-
||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.
 
|-
 
|-
||02.07
+
||02:07
 
||A Circle with center 'A' and radius '3cm' is drawn
 
||A Circle with center 'A' and radius '3cm' is drawn
  
 
|-
 
|-
||02.14
+
||02:14
 
||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
+
||02:36
 
||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
+
||02:45
 
||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
+
||02:52
 
||Perpendicular line and Chord 'BC' intersect at a point  
 
||Perpendicular line and Chord 'BC' intersect at a point  
 
|-
 
|-
||02.57
+
||02:57
 
||Click on “Intersect Two objects”  tool,
 
||Click on “Intersect Two objects”  tool,
  
 
|-
 
|-
||02.59
+
||02:59
 
||Mark the point of intersection as 'D'.
 
||Mark the point of intersection as 'D'.
 
|-
 
|-
||03.04
+
||03:04
 
||Let's verify whether D is the mid point of chord BC
 
||Let's verify whether D is the mid point of chord BC
 
|-
 
|-
||03.09
+
||03:09
 
||Click on the "Distance"  tool...
 
||Click on the "Distance"  tool...
  
 
|-
 
|-
||03.12
+
||03:12
 
||Click on the points ,'B'  'D' ...'D'  'C' ...
 
||Click on the points ,'B'  'D' ...'D'  'C' ...
  
 
|-
 
|-
||03.19
+
||03:19
 
||Notice that distances 'BD' and 'DC' are equal.
 
||Notice that distances 'BD' and 'DC' are equal.
  
 
|-
 
|-
||03.24
+
||03:24
 
||It implies 'D' is midpoint of  chord 'BC'
 
||It implies 'D' is midpoint of  chord 'BC'
 
|-
 
|-
||03.29
+
||03:29
 
||Let's measure the angle 'CDA'  
 
||Let's measure the angle 'CDA'  
  
 
|-
 
|-
||03.33
+
||03:33
 
||Click on Angle tool  ...
 
||Click on Angle tool  ...
  
 
|-
 
|-
||03.36
+
||03:36
 
||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 '90^0'.
 
|-
 
|-
||03.46
+
||03:46
 
|| TheTheorem is verified.
 
|| TheTheorem is verified.
 
|-
 
|-
||03.50
+
||03:50
 
||Let's Move the point  'C'  
 
||Let's Move the point  'C'  
  
 
|-
 
|-
||03.52
+
||03:52
 
||and see how the distances move along with point 'C'
 
||and see how the distances move along with point 'C'
  
 
|-
 
|-
||04.03
+
||04:03
 
||Let us save the file now
 
||Let us save the file now
 
|-
 
|-
||04.05
+
||04:05
 
||Click on  “File”>>  "Save As"
 
||Click on  “File”>>  "Save As"
  
 
|-
 
|-
||04.08
+
||04:08
 
||I will type the file name as "circle-chord" click on “Save”
 
||I will type the file name as "circle-chord" click on “Save”
 
|-
 
|-
||04.21
+
||04:21
 
||Let us move on to the next theorem.
 
||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.
 
||Let's verify the theorem.
 
|-
 
|-
||04.54
+
||04:54
 
||Let'sOpen a new Geogebra window,
 
||Let'sOpen 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 " the 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' and 'C'  on the circumference  
 
|-
 
|-
||05.09
+
||05:09
 
||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
+
||05:18
 
||Click on the point 'A'B' and 'C'  on the circumference  
 
||Click on the point 'A'B' and 'C'  on the circumference  
  
Line 262: Line 262:
  
 
|-
 
|-
||05.24
+
||05:24
 
||An Arc 'BC' is drawn  
 
||An Arc 'BC' is drawn  
 
|-
 
|-
||05.27
+
||05:27
 
||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
+
||05:38
 
||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
+
||06:04
 
||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
+
||06:27
 
||Click on the "Angle" tool,   
 
||Click on the "Angle" tool,   
  
 
|-
 
|-
||06.29
+
||06:29
 
||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
+
||06:52
 
||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 the measure 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 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 the tutorial  
 
|-
 
|-
||08.48
+
||08:48
 
||let's summarize
 
||let's summarize
 
|-
 
|-
||08.53
+
||08:53
 
||In this tutorial, we have learnt to verify that:
 
||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
+
|| 09:15
 
|| As an assignment  I would like you to verify  
 
|| As an assignment  I would like you to verify  
  
 
|-
 
|-
||09.19
+
||09:19
 
||Equal chords of a circle are equidistant from center.
 
||Equal chords of a circle are equidistant from center.
  
 
|-
 
|-
||09.24
+
||09:24
 
||Draw a circle.  
 
||Draw a circle.  
  
 
|-
 
|-
||09.26
+
||09:26
 
||Select Segment with Given length from point tool  
 
||Select Segment with Given length from point tool  
  
 
|-
 
|-
||09.29
+
||09:29
 
||Use it to draw two chords of equal size.  
 
||Use it to draw two chords of equal size.  
  
 
|-
 
|-
||09.33
+
||09:33
 
||Draw perpendicular lines from center  to chords.
 
||Draw perpendicular lines from center  to chords.
  
 
|-
 
|-
||09.37
+
||09:37
 
||Mark points of intersection.  
 
||Mark points of intersection.  
  
 
|-
 
|-
||09.40
+
||09:40
 
||Measure  perpendicular distances.  
 
||Measure  perpendicular distances.  
 
|-
 
|-
||09.44
+
||09:44
 
||Assignment  out put should look like this
 
||Assignment  out put 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 summarises 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 :
 
||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  
+
||10:07  
 
||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 http://spoken-tutorial.org/NMEICT-Intro ]
  
 
|-
 
|-
||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

Revision as of 12:24, 9 July 2014

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,
00:10 you will be able to verify theorems on
*Chords of circle.
  • Arcs of circle.
00:19 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
00:33 Ubuntu Linux OS Version 11.10 Geogebra Version 3.2.47.0
00:43 We will use the following Geogebra tools
00:47 * Circle with Center and Radius
00:50 * Circular Sector with Center between Two Points
00:53 * Circular Arc with Center between Two points
00:56 * Midpoint and
  • Perpendicular line
01:00 Let's open a new GeoGebra window.
01:02 Click on Dash home Media Apps.
01:07 Under Type Choose Education and GeoGebra.
01:15 Let's state a theorem
01:18 Perpendicular from center of circle to a chord bisects the chord
01:23 Perpendicular from center A of a circle to chord BC bisects it
01:32 Let's verify a 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'
01:45 uncheck 'Axes' and
01:47 Select 'Grid'
01:52 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 open
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
02:14 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'.
02:36 Click on "Perpendicular line" tool from tool bar
02:39 Click on the chord 'BC', and point 'A'.
02:45 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 Click on “Intersect Two objects” tool,
02:59 Mark the point of intersection as 'D'.
03:04 Let's verify whether D is the mid point of chord BC
03:09 Click on the "Distance" tool...
03:12 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 ...
03:36 Click on the points 'C','D', 'A'
03:42 angle 'CDA' is '90^0'.
03:46 TheTheorem is verified.
03:50 Let's Move the point 'C'
03:52 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" 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.
04:54 Let'sOpen a new Geogebra window,
04:51 Click on “File” >> "New"
04:55 Let's draw a circle
04:57 Click on " the 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' and 'C' on the circumference
05:09 Let's draw an arc 'BC'
05:13 Click on "Circular Arc with Center between Two points"
05:18 Click on the point 'A'B' and 'C' on the circumference


05:24 An Arc 'BC' is drawn
05:27 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"
05:38 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'.
06:04 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'
06:27 Click on the "Angle" tool,
06:29 Click on points 'B', 'D', 'C' and 'B', 'E', 'C'
06:40 We can see that the angles 'BDC' and 'BEC' are equal.
06:52 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 the measure 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 theorems are verified
08:45 With this we come to the end of the 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.
09:26 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 out put 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 summarises 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
10:07 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 http://spoken-tutorial.org/NMEICT-Intro ]
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