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

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(Created page with ' {|border =1 !Visual Cue !Narration |- ||00.01 ||Hello,Welcome to this tutorial on '''Theorems on Chords and Arcs in Geogebra''' |- ||00.08 ||At the end of this tutorial, |…')
 
 
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{|border =1
 
{|border =1
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!Visual Cue
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|'''Time'''
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!Narration   
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|'''Narration'''  
 
|-
 
|-
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||00.01
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||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
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||00:14
−
||you will be able to  verify theorems on
+
||Chords of circle.
  
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*Chords of circle.
 
−
 
−
* Arcs of circle.
 
 
|-
 
|-
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||00.19
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||00:16
−
||We assume that you have the basic working knowledge of Geogebra.   
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|| 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
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|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.
 
||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 now verify the 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.
 
||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
+
||02:52
−
||Perpendicular line and Chord 'BC' intersect at a point  
+
||Perpendicular line and chord '''BC''' intersect at a point.  
−
|-
+
−
||02.57
+
−
||Click on “Intersect Two objects”  tool,
+
  
 
|-
 
|-
−
||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'''.
 +
 
 +
|-
 +
||04:16
 +
|| 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
+
||04:48
−
||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:
 
||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.  
 
||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  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 :
 
||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.
  
 
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||Spoken Tutorial Project is a part  of the Talk to a Teacher project  
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||Spoken Tutorial Project is a part  of the Talk to a Teacher project.
  
 
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||This is Madhuri Ganapathi from IIT Bombay signing off .Thank you  for joining
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||This is Madhuri Ganapathi from IIT Bombay, signing off .Thank you  for joining.

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

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