Geogebra/C3/Theorems-on-Chords-and-Arcs/English-timed
From Script | Spoken-Tutorial
| 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. |
