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The longest chord passes through the centre of the circle (view source)
Revision as of 06:51, 4 December 2013
, 06:51, 4 December 2013→Activity No # Construction of Direct common tangent
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*Estimated Time
*Estimated Time: 90 minutes
*Materials/ Resources needed
*Materials/ Resources needed:
# Laptop, geogebra file, projector and a pointer.
# Students' individual construction materials.
*Prerequisites/Instructions, if any
*Prerequisites/Instructions, if any
*Multimedia resources
# 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:
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:
[Note for teachers : Evaluate if it is possible to construct a direct common tangent without the third circle.]
# 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 # Construction of Transverse common tangent===
===Activity No # Construction of Transverse common tangent===