Difference between revisions of "Geogebra/C3/Tangents-to-a-circle/English-timed"
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| − | |Select "Perpendicular Bisector" tool, Click on the points 'A' & 'B' | + | |Select "Perpendicular Bisector" tool, Click on the points 'A' & 'B'.Perpendicular bisector to segment 'AB' is drawn. |
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| − | |Mark point of intersection as 'C' Let's Move point 'B',& | + | |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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Revision as of 14:07, 12 February 2013
| 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 dialogue box opens. |
| 01.53 | 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 point" tool,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,C lick 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' Lets 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' & 'C' 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 tangents & 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 point'C' 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 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' & 'C' 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 an circle, is supplementary to the angle subtended by the line-segment 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 about 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 segments bisects the angle.
|
| 10.16 | Watch the video available at this url http://spoken-tutorial.org/ |
| 10.19 | It summarises 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 http://spoken-tutorial.org/NMEICT-Intro ] |
| 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
