Difference between revisions of "Geogebra/C3/Tangents-to-a-circle/English-timed"
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|00:00 | |00:00 | ||
− | |Hello Welcome to this tutorial on '''Tangents to a circle in Geogebra'''. | + | |Hello. Welcome to this tutorial on '''Tangents to a circle in Geogebra'''. |
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|00:06 | |00:06 | ||
− | |At the end of this tutorial you will be able to | + | |At the end of this tutorial, you will be able to draw tangents to the circle, understand the properties of tangents. |
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|00:22 | |00:22 | ||
− | |If not, | + | |If not, for relevant tutorials, please visit our website http://spoken-tutorial.org. |
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|00:27 | |00:27 | ||
− | |To record this tutorial, I am using Ubuntu Linux OS Version 11.10, Geogebra Version 3.2.47.0 . | + | |To record this tutorial, I am using '''Ubuntu Linux OS Version 11.10, Geogebra Version 3.2.47.0'''. |
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|00:41 | |00:41 | ||
− | |We will use the following Geogebra tools | + | |We will use the following Geogebra tools: Tangents, Perpendicular Bisector |
− | + | ||
− | + | Intersect two Objects, Compass, Polygon & Circle with Center and Radius. | |
− | + | ||
− | + | ||
− | + | ||
− | + | ||
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|00:58 | |00:58 | ||
− | |Let's open a new | + | |Let's open a new Geogebra window. |
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|01:01 | |01:01 | ||
− | |Click on Dash home Media Applications. Under Type | + | |Click on '''Dash home''' >> '''Media Applications'''. Under '''Type''', choose '''Education''' and '''GeoGebra'''. |
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|01:13 | |01:13 | ||
− | | | + | |Let's define tangents to a circle. |
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|01:16 | |01:16 | ||
− | |Tangent is a line that touches a circle at only one point. | + | |"Tangent is a line that touches a circle at only one point". |
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|01:22 | |01:22 | ||
− | |The point of contact is called | + | |The point of contact is called "point of tangency". |
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|01:27 | |01:27 | ||
− | |For this tutorial I will use '''Grid''' layout instead of "Axes", | + | |For this tutorial, I will use '''Grid''' layout instead of "Axes", right click on the drawing pad. |
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|01:35 | |01:35 | ||
− | | | + | |Uncheck '''Axes''', select '''Grid'''. |
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|01:39 | |01:39 | ||
− | | | + | | Let us draw tangent to a circle. |
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|01:52 | |01:52 | ||
− | |A | + | |A dialog box opens. Let's type value '''3''' for radius, click '''OK'''. |
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− | + | ||
− | + | ||
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|02:04 | |02:04 | ||
− | |Let's | + | |Let's move the point '''A''' & see that circle has same radius. |
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|02:09 | |02:09 | ||
− | |Click on the '''New | + | |Click on the '''New Point'''tool. Mark a point '''B''' outside the circle. |
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|02:15 | |02:15 | ||
− | | | + | |Select '''Segment between Two Points''' tool. Join points '''A''' and '''B'''. A segment '''AB''' is drawn. |
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|02:25 | |02:25 | ||
− | |Select '''Perpendicular Bisector''' tool, | + | |Select '''Perpendicular Bisector''' tool, click on the points '''A''' & '''B'''. Perpendicular bisector to segment '''AB''' is drawn. |
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|02:37 | |02:37 | ||
− | |Segment '''AB''' and | + | |Segment '''AB''' and perpendicular bisector intersect at a point. Click on '''Intersect Two Objects''' tool. |
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|02:44 | |02:44 | ||
− | |Mark point of intersection as '''C''' Let's | + | |Mark point of intersection as '''C'''. Let's move point '''B''' & see how the perpendicular bisector and point '''C''' move along with point '''B'''. |
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|03:02 | |03:02 | ||
− | |Click on '''Distance''' tool. | + | |Click on '''Distance''' tool. Click on the points '''A''' , '''C''', '''C''' ,'''B'''. Notice that '''AC''' = '''CB''' implies '''C''' is the midpoint of '''AB'''. |
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|03:20 | |03:20 | ||
− | |Select '''Compass''' tool from tool bar, | + | |Select '''Compass''' tool from tool bar, click on the points '''C''', '''B''' and '''C''' once again... to complete the figure. |
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|03:30 | |03:30 | ||
|Two circles intersect at two points. | |Two circles intersect at two points. | ||
− | |||
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|03:33 | |03:33 | ||
− | |Click on the '''Intersect | + | |Click on the '''Intersect Two Objects''' tool. Mark the points of intersection as '''D''' and '''E'''. |
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|03:42 | |03:42 | ||
− | |Select '''Segment between | + | |Select '''Segment between Two Points''' tool. |
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|03:53 | |03:53 | ||
− | |Segments '''BD''' and '''BE''' are tangents to the circle '''c''' | + | |Segments '''BD''' and '''BE''' are tangents to the circle '''c'''. |
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|03:59 | |03:59 | ||
− | | | + | | Let's explore some of the properties of these tangents to the circle. |
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|04:05 | |04:05 | ||
− | |Select '''Segment between | + | |Select '''Segment between Two Points''' tool. |
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|04:14 | |04:14 | ||
− | |In triangles '''ADB''' and '''ABE''' | + | |In triangles '''ADB''' and '''ABE''', segment '''AD'''= segment '''AE''' (radii of the circle 'c'). |
− | Let's see from the Algebra | + | Let's see from the '''Algebra View''' that segment '''AD'''= segment '''AE'''. |
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|04:34 | |04:34 | ||
− | |'''∠ADB'''= '''∠BEA''' | + | |'''∠ADB'''= '''∠BEA''', angle of the semicircle of circle '''d'''. Let's measure the angle. |
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|04:48 | |04:48 | ||
− | |Click on the '''Angle''' tool | + | |Click on the '''Angle''' tool. Click on the points '''A''', '''D''', '''B''' and '''B''', '''E''', '''A''', angles are equal. |
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|05:03 | |05:03 | ||
− | |Segment '''AB''' is common to both the triangles,therefore '''△ADB''' '≅' '''△ABE''' by '''SAS rule of congruency''' | + | |Segment '''AB''' is common to both the triangles, therefore '''△ADB''' '≅' '''△ABE''' by '''SAS rule of congruency'''. |
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|05:20 | |05:20 | ||
− | |It implies | + | |It implies: tangents '''BD''' and '''BE''' are equal! |
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|05:26 | |05:26 | ||
− | |From the Algebra | + | |From the '''Algebra View''', we can find that tangents '''BD''' and '''BE''' are equal. |
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|05:33 | |05:33 | ||
− | |Please | + | |Please notice that tangent is always at right angles to the radius of the circle where it touches. |
− | + | Let us move the point '''B''' & see how the tangents move along with point '''B'''. | |
− | Let us move the point '''B''' & | + | |
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|05:50 | |05:50 | ||
− | |Let us save the file now. Click on '''File'''>> '''Save As''' | + | |Let us save the file now. Click on '''File'''>> '''Save As'''. |
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|05:54 | |05:54 | ||
− | |I will type the file name as '''Tangent-circle''' Click on '''Save''' | + | |I will type the file name as '''Tangent-circle'''. Click on '''Save'''. |
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|06:08 | |06:08 | ||
− | |Let's state a theorem | + | |Let's state a theorem. |
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|06:11 | |06:11 | ||
− | | | + | |"Angle between tangent and chord at the point of tangency is same as an inscribed angle subtended by the same chord". |
− | + | Angle DFB between tangent & chord = inscribed angle FCB of the chord BF. | |
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|06:34 | |06:34 | ||
− | |Let's verify the theorem | + | |Let's verify the theorem. |
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|06:38 | |06:38 | ||
− | |Let's open a new Geogebra window. | + | |Let's open a new Geogebra window. Click on '''File''' >> '''New'''. Let's draw a circle. |
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|06:48 | |06:48 | ||
− | |Click on the '''Circle with | + | |Click on the '''Circle with Center through Point''' tool from tool bar . Mark a point '''A''' as a centre and click again to get '''B'''. |
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|06:59 | |06:59 | ||
− | |Select '''New | + | |Select '''New Point''' tool. Mark point'''C''' on the circumference and '''D''' outside the circle. |
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|07:06 | |07:06 | ||
− | |Select '''Tangents''' tool from toolbar. | + | |Select '''Tangents''' tool from toolbar. Click on the point '''D''' and on circumference. |
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|07:14 | |07:14 | ||
− | |Two | + | |Two tangents are drawn to the circle. |
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|07:20 | |07:20 | ||
− | |Click on the '''Intersect | + | |Click on the '''Intersect Two Objects''' tool. Mark points of contact as '''E''' and '''F'''. |
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|07:28 | |07:28 | ||
− | |Let's draw a triangle.Click on the '''Polygon''' tool. | + | |Let's draw a triangle. Click on the '''Polygon''' tool. |
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|07:31 | |07:31 | ||
− | |Click on the points '''B''' '''C''' '''F''' and '''B''' once again to complete the figure. | + | |Click on the points '''B''', '''C''', '''F''' and '''B''' once again to complete the figure. |
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|07:41 | |07:41 | ||
− | |In the figure '''BF''' is the chord to the circle '''c'''. | + | |In the figure, '''BF''' is the chord to the circle '''c'''. |
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|07:53 | |07:53 | ||
− | |'''∠DFB''' is angle between tangent and chord to the circle '''c'''. | + | |'''∠DFB''' is the angle between tangent and chord to the circle '''c'''. |
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|08:01 | |08:01 | ||
− | |Lets | + | |Lets measure the angles, click on the '''Angle''' tool, click on the points '''D''', '''F''', '''B''' and '''F''', '''C''', '''B'''. |
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|08:14 | |08:14 | ||
− | |Notice that '''∠DFB''' = '''∠FCB'''. Let us move the point '''D''' & | + | |Notice that '''∠DFB''' = '''∠FCB'''. Let us move the point '''D''' & see that tangents and chords move along with point 'D'. |
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|08:31 | |08:31 | ||
− | |Let us save the file now.Click on '''File'''>> '''Save As''' | + | |Let us save the file now. Click on '''File''' >> '''Save As'''. |
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|08:36 | |08:36 | ||
− | |I will type the file name as '''Tangent-angle''' Click on '''Save''' With this we come to the end of this tutorial. | + | |I will type the file name as '''Tangent-angle'''. Click on '''Save'''. With this, we come to the end of this tutorial. |
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|08:50 | |08:50 | ||
− | |Let's summarize | + | |Let's summarize. In this tutorial, we have learnt to verify that: |
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|08:57 | |08:57 | ||
− | | | + | |Two tangents drawn from an external point are equal |
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|09:01 | |09:01 | ||
− | | | + | |Angle between a tangent and radius of a circle is 90^0. |
|- | |- | ||
|09:07 | |09:07 | ||
− | | | + | |Angle between tangent and a chord is equal to inscribed angle subtended by the chord. |
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|09:14 | |09:14 | ||
− | |As an assignment I would like you to verify: | + | |As an assignment, I would like you to verify: |
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|09:17 | |09:17 | ||
− | | | + | |"Angle between tangents drawn to a circle, is supplementary to the angle subtended by the line segments joining the points of contact at the centre". |
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|09:30 | |09:30 | ||
− | |To verify | + | |To verify: Draw a circle. Draw tangents from an external point. |
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|09:44 | |09:44 | ||
− | |Measure angle at the centre, | + | |Measure angle at the centre, measure angle between the tangents. |
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|09:49 | |09:49 | ||
− | |What is the sum of | + | |What is the sum of above two angles? Join centre and external point. |
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|09:55 | |09:55 | ||
− | |Does the line-segment bisect the angle at the centre? Hint - Use Angle Bisector tool. | + | |Does the line-segment bisect the angle at the centre? Hint - Use '''Angle Bisector''' tool. |
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|10:05 | |10:05 | ||
− | |The output | + | |The output should look like this. |
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|10:08 | |10:08 | ||
− | |Sum of the angles is 180^0. The line | + | |Sum of the angles is 180^0. The line segment bisects the angle. |
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|10:19 | |10:19 | ||
− | |It | + | |It summarizes the Spoken Tutorial project. If you do not have good bandwidth, you can download and watch it. |
|- | |- | ||
|10:27 | |10:27 | ||
− | |The Spoken tutorial project team Conducts workshops using spoken tutorials. | + | |The Spoken tutorial project team: Conducts workshops using spoken tutorials. |
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|10:54 | |10:54 | ||
− | |More information on this | + | |More information on this mission is available at this link [http://spoken-tutorial.org/NMEICT-Intro]. |
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|This is Madhuri Ganpathi from IIT Bombay. | |This is Madhuri Ganpathi from IIT Bombay. | ||
− | Thank you for joining | + | Thank you for joining. |
Latest revision as of 14:39, 28 October 2020
Time | Narration |
00:00 | Hello. Welcome to this tutorial on Tangents to a circle in Geogebra. |
00:06 | At the end of this tutorial, you will be able to draw tangents to the circle, understand the properties of tangents. |
00:17 | We assume that you have the basic working knowledge of Geogebra. |
00:22 | If not, for relevant tutorials, please visit our website http://spoken-tutorial.org. |
00:27 | To record this tutorial, I am using Ubuntu Linux OS Version 11.10, Geogebra Version 3.2.47.0. |
00:41 | We will use the following Geogebra tools: Tangents, Perpendicular Bisector
Intersect two Objects, Compass, Polygon & Circle with Center and Radius. |
00:58 | Let's open a new Geogebra window. |
01:01 | Click on Dash home >> Media Applications. Under Type, choose Education and GeoGebra. |
01:13 | Let's define tangents to a circle. |
01:16 | "Tangent is a line that touches a circle at only one point". |
01:22 | The point of contact is called "point of tangency". |
01:27 | For this tutorial, I will use Grid layout instead of "Axes", right click on the drawing pad. |
01:35 | Uncheck Axes, select Grid. |
01:39 | Let us draw tangent to a circle. |
01:42 | First let us draw a circle. |
01:45 | Select Circle with Center and Radius tool from toolbar. |
01:49 | Mark a point A on the drawing pad. |
01:52 | A dialog box opens. Let's type value 3 for radius, click OK. |
01:58 | A circle with centre A and radius 3 cm is drawn. |
02:04 | Let's move the point A & see that circle has same radius. |
02:09 | Click on the New Pointtool. Mark a point B outside the circle. |
02:15 | Select Segment between Two Points tool. Join points A and B. A segment AB is drawn. |
02:25 | Select Perpendicular Bisector tool, click on the points A & B. Perpendicular bisector to segment AB is drawn. |
02:37 | Segment AB and perpendicular bisector intersect at a point. Click on Intersect Two Objects tool. |
02:44 | Mark point of intersection as C. Let's move point B & see how the perpendicular bisector and point C move along with point B. |
02:59 | How to verify C is the midpoint of AB? |
03:02 | Click on Distance tool. Click on the points A , C, C ,B. Notice that AC = CB implies C is the midpoint of AB. |
03:20 | Select Compass tool from tool bar, click on the points C, B and C once again... to complete the figure. |
03:30 | Two circles intersect at two points. |
03:33 | Click on the Intersect Two Objects tool. Mark the points of intersection as D and E. |
03:42 | Select Segment between Two Points tool. |
03:45 | Join points B, D and B , E . |
03:53 | Segments BD and BE are tangents to the circle c. |
03:59 | Let's explore some of the properties of these tangents to the circle. |
04:05 | Select Segment between Two Points tool. |
04:08 | Join points A, D and A, E. |
04:14 | In triangles ADB and ABE, segment AD= segment AE (radii of the circle 'c').
Let's see from the Algebra View that segment AD= segment AE. |
04:34 | ∠ADB= ∠BEA, angle of the semicircle of circle d. Let's measure the angle. |
04:48 | Click on the Angle tool. Click on the points A, D, B and B, E, A, angles are equal. |
05:03 | Segment AB is common to both the triangles, therefore △ADB '≅' △ABE by SAS rule of congruency. |
05:20 | It implies: tangents BD and BE are equal! |
05:26 | From the Algebra View, we can find that tangents BD and BE are equal. |
05:33 | Please notice that tangent is always at right angles to the radius of the circle where it touches.
Let us move the point B & see how the tangents move along with point B. |
05:50 | Let us save the file now. Click on File>> Save As. |
05:54 | I will type the file name as Tangent-circle. Click on Save. |
06:08 | Let's state a theorem. |
06:11 | "Angle between tangent and chord at the point of tangency is same as an inscribed angle subtended by the same chord".
Angle DFB between tangent & chord = inscribed angle FCB of the chord BF. |
06:34 | Let's verify the theorem. |
06:38 | Let's open a new Geogebra window. Click on File >> New. Let's draw a circle. |
06:48 | Click on the Circle with Center through Point tool from tool bar . Mark a point A as a centre and click again to get B. |
06:59 | Select New Point tool. Mark pointC on the circumference and D outside the circle. |
07:06 | Select Tangents tool from toolbar. Click on the point D and on circumference. |
07:14 | Two tangents are drawn to the circle. |
07:16 | Tangents meet at two points on the circle. |
07:20 | Click on the Intersect Two Objects tool. Mark points of contact as E and F. |
07:28 | Let's draw a triangle. Click on the Polygon tool. |
07:31 | Click on the points B, C, F and B once again to complete the figure. |
07:41 | In the figure, BF is the chord to the circle c. |
07:45 | ∠FCB is the inscribed angle by the chord to the circle c. |
07:53 | ∠DFB is the angle between tangent and chord to the circle c. |
08:01 | Lets measure the angles, click on the Angle tool, click on the points D, F, B and F, C, B. |
08:14 | Notice that ∠DFB = ∠FCB. Let us move the point D & see that tangents and chords move along with point 'D'. |
08:31 | Let us save the file now. Click on File >> Save As. |
08:36 | I will type the file name as Tangent-angle. Click on Save. With this, we come to the end of this tutorial. |
08:50 | Let's summarize. In this tutorial, we have learnt to verify that: |
08:57 | Two tangents drawn from an external point are equal |
09:01 | Angle between a tangent and radius of a circle is 90^0. |
09:07 | Angle between tangent and a chord is equal to inscribed angle subtended by the chord. |
09:14 | As an assignment, I would like you to verify: |
09:17 | "Angle between tangents drawn to a circle, is supplementary to the angle subtended by the line segments joining the points of contact at the centre". |
09:30 | To verify: Draw a circle. Draw tangents from an external point. |
09:37 | Mark points of contact of the tangents. Join centre of circle to points of contact. |
09:44 | Measure angle at the centre, measure angle between the tangents. |
09:49 | What is the sum of above two angles? Join centre and external point. |
09:55 | Does the line-segment bisect the angle at the centre? Hint - Use Angle Bisector tool. |
10:05 | The output should look like this. |
10:08 | Sum of the angles is 180^0. The line segment bisects the angle. |
10:16 | Watch the video available at this url http://spoken-tutorial.org/ |
10:19 | It summarizes the Spoken Tutorial project. If you do not have good bandwidth, you can download and watch it. |
10:27 | The Spoken tutorial project team: Conducts workshops using spoken tutorials. |
10:32 | Gives certificates to those who pass an online test. |
10:35 | For more details, please write to contact@spoken-tutorial.org. |
10:42 | Spoken Tutorial Project is a part of Talk to a Teacher project. |
10:47 | It is supported by the National Mission on Education through ICT, MHRD, Government of India. |
10:54 | More information on this mission is available at this link [1]. |
10:59 | The script is contributed by Neeta Sawant from SNDT Mumbai. |
11:04 | This is Madhuri Ganpathi from IIT Bombay.
Thank you for joining. |
Contributors and Content Editors
Madhurig, Minal, PoojaMoolya, Pratik kamble, Sakinashaikh, Sandhya.np14, Sneha