Geogebra/C3/Theorems-on-Chords-and-Arcs/Gujarati

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,
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	આ યુઆરએલ પર ઉપલબ્ધ વિડીયો નિહાળો http://spoken-tutorial.org/What is a Spoken Tutorial
09.51	તે સ્પોકન ટ્યુટોરીયલ પ્રોજેક્ટનો સારાંશ આપે છે
09.53	જો તમારી બેન્ડવિડ્થ સારી ન હોય, તો તમે ડાઉનલોડ કરી તે જોઈ શકો છો
09.58	સ્પોકન ટ્યુટોરીયલ પ્રોજેક્ટ ટીમ :
10.00	સ્પોકન ટ્યુટોરીયલોનાં મદદથી વર્કશોપોનું આયોજન કરે છે
10.03	જેઓ ઓનલાઈન પરીક્ષા પાસ કરે છે તેમને પ્રમાણપત્રો આપે છે
10.07	વધુ વિગત માટે, કૃપા કરી contact@spoken-tutorial.org પર સંપર્ક કરો
10.14	સ્પોકન ટ્યુટોરીયલ પ્રોજેક્ટ એ ટોક ટુ અ ટીચર પ્રોજેક્ટનો એક ભાગ છે
10.18	જે આઇસીટી, એમએચઆરડી, ભારત સરકાર દ્વારા શિક્ષણ પર નેશનલ મિશન દ્વારા આધારભૂત છે
10.25	આ મિશન પર વધુ માહીતી http://spoken-tutorial.org/NMEICT-Intro લીંક પર ઉપલબ્ધ છે
10.29	IIT-Bombay તરફથી સ્પોકન ટ્યુટોરીયલ પ્રોજેક્ટ માટે ભાષાંતર કરનાર હું, જ્યોતી સોલંકી વિદાય લઉં છું. જોડાવાબદ્દલ આભાર.

Contributors and Content Editors

Jyotisolanki, PoojaMoolya