1,040
edits
Changes
Jump to navigation
Jump to search
Line 152:
Line 152: − + − + − + − + − + + + + + + + + + + + + + − + − + − + − + + + + + + + + + + + + + + + + + + + + + + + + + +
→Activity No #
*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.===
{| style="height:10px; float:right; align:center;"
{| style="height:10px; float:right; align:center;"
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;">
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
''[http://www.karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
|}
|}
*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 # ===