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##
Circles Constructions
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Revision as of 09:17, 2 November 2013

2,580 bytes added
, 09:17, 2 November 2013

→Activity No #

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*Evaluation

*Evaluation

*Question Corner

*Question Corner

−===Activity No # ===

+===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

+*Estimated Time: 90 minutes

−*Materials/ Resources needed

+*Materials/ Resources needed: # Laptop, geogebra file, projector and a pointer.

−*Prerequisites/Instructions, if any

+# Students' individual construction materials.

−*Multimedia resources

+*Prerequisites/Instructions, if any:

+# The students should have prior knowledge of a circle , tangent and the limiting case of a

+ secant as a tangent.

+# They should understand that a tangent is always perpendicular to the radius of the circle.

+# They should know construction of a tangent to a given point.

+# If the same straight line is a tangent to two or more circles, then it is called a common tangent.

+# If the centres of the circles lie on the same side of the common tangent, then the tangent is called a direct common tangent.

+# Note: In general,

+*The two circles are named as C1 and C2

+* The distance between the centre of two circles is 'd'

+* Radius of one circle is taken as 'R' and other as 'r'

+* The length of tangent is 't'

+*Multimedia resources: Laptop

*Website interactives/ links/ / Geogebra Applets

*Website interactives/ links/ / Geogebra Applets

−*Process~~/ ~~Developmental Questions

+*Process:

−*Evaluation

+[Note for teachers : Evaluate if it is possible to construct a direct common tangent without the third circle.]<br>

−*Question Corner

+The teacher can explain the step by step construction of Direct common tangent and with an example

−*Developmental Questions:

+# What is a tangent

+# What is a common tangent ?

+# What is a direct common tangent ?

+# What is R and r ?

+# What does the length OA represent here ?

+# Why was a third circle constructed ?

+# Let us try to construct direct common tangent without the third circle and see.

+# What should be the radius of the third circle ?

+# Why was OA bisected and semi circle constructed ?

+# What were OB and OC extended ?

+# What can you say about lines AB and AC ?

+# Name the direct common tangents .

+# At what points is the tangent touching the circles ?

+# Identify the two right angled triangles formed from the figure ? What do you understand ?

+*Evaluation:

+# Is the student able to comprehend the sequence of steps in constructing the tangent.

+# Is the student able to identify error areas while constructing ?

+# Is the student observing that the angle between the tangent and radius at the point of intersection is 90º ?

+# 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.

+*Question Corner:

+# What do you think are the applications of tangent constructions ?

+# What is the formula to find the length of direct common tangent ?

+# Can a direct common tangent be drawn to two circles one inside the other ?

+# Observe the point of intersection of extended tangents in relation with the centres of two circles. Infer.

+# What are properties of direct common tangents ?

===Activity No # ===

===Activity No # ===

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