# Changes

,  09:17, 2 November 2013
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*Evaluation

*Evaluation

*Question Corner

*Question Corner
===Activity No # ===
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===Activity No # Construct a direct common tangent to two circles with given radii and given distance between the centre of two circles.===

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''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>

''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>

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*Estimated Time
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*Estimated Time: 90 minutes
*Materials/ Resources needed
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*Materials/ Resources needed: # Laptop, geogebra file, projector and a pointer.
*Prerequisites/Instructions, if any
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# Students' individual construction materials.
*Multimedia resources
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*Prerequisites/Instructions, if any:
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# The students should have prior knowledge of a circle , tangent and the limiting case of a
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secant as a tangent.
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# They should understand that a tangent is always perpendicular to the radius of the circle.
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# They should know construction of a tangent to a given point.
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# If the same straight line is a tangent to two or more circles, then it is called a common tangent.
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# If the centres of the circles lie on the same side of the common tangent, then the tangent is called a direct common tangent.
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# Note: In general,
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*The two circles are named as C1 and C2
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* The distance between the centre of two circles is 'd'
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* Radius of one circle is taken as 'R' and other as 'r'
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* The length of tangent is 't'
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*Multimedia resources: Laptop

*Website interactives/ links/ / Geogebra Applets

*Website interactives/ links/ / Geogebra Applets
*Process/ Developmental Questions
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*Process:
*Evaluation
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[Note for  teachers : Evaluate if it is possible to construct a direct common tangent without the third circle.]<br>
*Question Corner
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The teacher can explain the step by step construction of Direct common tangent  and with an example

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*Developmental Questions:
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# What is a tangent
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# What is a common tangent ?
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# What is a direct common tangent ?
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# What is R and r  ?
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# What does the length OA represent here ?
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# Why was a third circle constructed ?
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# Let us try to construct direct common tangent without the third circle and see.
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# What should be the radius of the third circle ?
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# Why was OA bisected and semi circle constructed ?
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# What were OB and OC extended ?
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# What can you say about lines AB and AC ?
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# Name the direct common tangents .
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# At what points is the tangent touching the circles ?
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# Identify the two right angled triangles formed from the figure ? What do you understand ?
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*Evaluation:
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# Is the student able to comprehend the sequence of steps in constructing the tangent.
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# Is the student able to identify error areas while constructing ?
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# Is the student observing that the angle between the tangent and radius at the point of intersection is 90º ?
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# Is the student able to appreciate that the direct common tangents from the same external point are equal and subtend equal angles at the center.
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*Question Corner:
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# What do you think are the applications of tangent constructions ?
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# What is the formula to find the length of direct common tangent ?
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# Can a direct common tangent be drawn to two circles one inside the other ?
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# Observe the point of intersection of extended tangents in relation with the centres of two circles. Infer.
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# What are properties of direct common tangents ?

===Activity No # ===

===Activity No # ===
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