View source for Geogebra/C3/Theorems-on-Chords-and-Arcs/English-timed

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|'''Time'''
|'''Narration'''  
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||Hello,Welcome to this  tutorial on '''Theorems on Chords and Arcs in Geogebra'''
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||At the end of this  tutorial, 

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||you will be able to  verify theorems on 

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||Chords of circle.

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|| Arcs of circle.
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||We assume that you have the basic working knowledge of Geogebra.  

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||If not, For relevant tutorials, please visit our website:  http://spoken-tutorial.org
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||To record this tutorial I am using  

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||Ubuntu Linux OS Version  11.10  

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||Geogebra Version 3.2.47.0 

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||We will use the following Geogebra tools  
    
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||* Circle with Center and Radius 

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||* Circular Sector with Center between Two Points

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||* Circular Arc with Center between Two points

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||* Midpoint  and

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||Perpendicular line 
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||Let's open a new  GeoGebra window.

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||Click on  Dash  home,  Media Apps.

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||Under Type Choose Education and  GeoGebra.

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||Let's state a  theorem

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||   '''Perpendicular from center of  circle to a chord bisects the chord'''

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||'''Perpendicular from the center A   of a circle to chord BC bisects it'''

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||Let's verify a theorem.

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||For this tutorial  I will use '''Grid layout''' instead of Axes

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||Right Click on the drawing pad 

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||In the '''Graphic view''' uncheck '''Axes''' 

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||Select '''Grid'''
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||Let's draw a circle.

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||Select the '''Circle with Center and Radius'''  tool from tool bar. 

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||Mark a point '''A'''  on the drawing pad.
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||A dialogue box   opens
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||Let's type value '''3''' for radius 

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||Click '''OK'''.
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||A Circle with center '''A''' and radius '''3cm''' is drawn

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||Let's Move the  point '''A''' and  see the movement of the circle.
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||Select  '''Segment between two points''' tool. 

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||Mark points '''B'''  and '''C'''  on the circumference of the circle 

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||A chord '''BC''' is drawn.

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||Let's draw a  perpendicular line to Chord '''BC'''  which passes through point '''A'''

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||Click on  '''Perpendicular line'''  tool from tool bar

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||Click on  the chord  '''BC''', and point '''A'''.

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||Let's Move the  point '''B''', and see how the perpendicular line moves along with point 'B'.

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||Perpendicular line and Chord '''BC''' intersect at a point 

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||Click on '''Intersect Two objects'''  tool,

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||Mark the point of intersection as '''D'''.

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||Let's verify whether '''D''' is the mid point of chord '''BC'''

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||Click on the '''Distance''' tool.

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||Click on the points ,'''B'''  '''D''' ...'''D'''  '''C''' ...

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||Notice that distances '''BD''' and '''DC''' are equal.

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||It implies '''D''' is midpoint of  chord '''BC'''
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||Let's measure the angle '''CDA''' 

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||Click on Angle tool  ...

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||Click on the points '''C''','''D''', '''A''' 

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||  angle '''CDA''' is '90 degrees

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|| The Theorem is verified.

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||Let's Move the point  '''C'''  and see how the distances move along with point 'C'

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||Let us save the file now

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||Click on  '''File'''>>  '''Save As'''

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||I will type the file name as '''circle-chord''' 

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||'''circle-chord'''

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|| Click on '''Save'''

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||Let us move on to the next theorem.

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||'''Inscribed angles subtended by the same arc are equal.'''   

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||'''Inscribed angles BDC and BEC subtended by the same arc BC are equal'''  
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||Let's verify the theorem.
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||Let'sOpen a new Geogebra window,

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||Click on '''File''' >> '''New'''
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||Let's draw a circle

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||Click on '''the Circle with Center through Point''' tool from toolbar

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||Mark a point A' as centre 

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|| and click again to get point '''B''' 

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||Let's draw an arc '''BC'''

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||Click on "'''Circular Arc with Center between Two points"'''

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||Click on the point '''A''',  '''B''' and '''C'''  on the circumference 

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||An Arc '''BC''' is drawn 

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||Let's change the  properties of arc '''BC'''
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||In the '''Algebra View''' 

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||Right click on the object '''d'''

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||Select  '''Object Properties'''

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||Select color as '''green''',  click on '''Close.'''
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|| Click on '''new point tool''', mark points  '''D''' and '''E''' on the circumference of the circle.

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||let's subtend two angles from arc BC to points  '''D''' and '''E'''.

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||Click on '''Polygon''' tool, 
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||click on the  points  '''E''', '''B''', '''D''', '''C''' and '''E'''  again to complete the figure.
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||Let's measure the angles  '''BDC'''  and '''BEC''' 

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||Click on the '''Angle''' tool,  

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||Click  on points  '''B''', '''D''', '''C''' and     '''B''', '''E''', '''C'''
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||We can see that the angles  '''BDC'''  and  '''BEC''' are equal.
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||Let's state a next theorem
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||'''Angle subtended by an arc at the center, is twice the  inscribed angles subtended by the same arc'''   
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||'''Angle BAC subtended by arc BC at A is twice the inscribed angles BEC and BDC subtended by the same  arc'''
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||Let's verify the theorem
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||Let's draw a sector '''ABC'''

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||Click on the '''Circular Sector with Center between Two Points''' tool.

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||click on the  points '''A''',  '''B''', '''C'''
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||Let's change the color of   sector '''ABC'''.

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||Right click on sector '''ABC'''

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||Select '''Object Properties'''.

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||Select Color as '''Green'''. Click on '''Close'''.
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||Let's the measure angle '''BAC'''

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||Click on  the '''Angle''' tool , Click on the points '''B''', '''A''', '''C'''

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||Angle  '''BAC''' is twice the angles  '''BEC''' and '''BDC'''
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||Let's move the point '''C'''

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||Notice that   angle  '''BAC''' is always twice the angles  '''BEC''' and '''BDC'''

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||hence theorems  are verified

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||With this we come to the end of this tutorial 

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||let's summarize

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||In this tutorial, we have learnt to verify that:

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||*  Perpendicular   from center to a  chord bisects it 

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||*  Inscribed angles subtended by the same  arc  are equal 

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||* the Central angle of a circle is twice any inscribed angle subtended by the same arc

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|| As an assignment  I would like you to verify 

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||Equal chords of a circle are equidistant from center.

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||Draw a circle. 

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||Select Segment with Given length from point tool 

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||Use it to draw two chords of equal size. 

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||Draw perpendicular lines from center  to chords.

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||Mark points of intersection. 

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||Measure  perpendicular distances. 
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||Assignment  output should look like this
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||09:48
||Watch the video available at this url:  http://spoken-tutorial.org/What is a Spoken Tutorial 

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||09:51
||It summarises the Spoken Tutorial project 

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||09:53
||If you do not have good bandwidth, you can download and watch it 

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||09:58
||The Spoken Tutorial Project Team :

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||Conducts workshops using spoken tutorials 

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||Gives certificates to those who pass an online test 

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||For more details, please write to contact@spoken-tutorial.org
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||Spoken Tutorial Project is a part  of the Talk to a Teacher project 

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||It is supported by the National Mission on Education through ICT, MHRD, Government of India 

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||More information on this Mission is available at this link

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||This is Madhuri Ganapathi from IIT Bombay signing off .Thank you  for joining