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

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Revision as of 11:53, 9 September 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,
00:09 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 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 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 dialogue box opens
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
02:13 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'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
05:10 Let's draw an arc BC
05:13 Click on "Circular Arc with Center between Two points"
05:17 Click on the point 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 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 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.
09:25 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 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
10:06 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