# Difference between revisions of "Circles Constructions"

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# Concept Map

Error: Mind Map file `Circles_Constructions.mm` not found

# Textbook

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# Teaching Outlines

## Concept #1. Construction of chord.

### Activity No #

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## Concept #2. Construction of Tangent.

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## Concept #3. Construction of direct common tangent.

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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.

• Estimated Time: 90 minutes
• Materials/ Resources needed: # Laptop, geogebra file, projector and a pointer.
1. Students' individual construction materials.
• Prerequisites/Instructions, if any:
1. The students should have prior knowledge of a circle , tangent and the limiting case of a

secant as a tangent.

1. They should understand that a tangent is always perpendicular to the radius of the circle.
2. They should know construction of a tangent to a given point.
3. If the same straight line is a tangent to two or more circles, then it is called a common tangent.
4. If the centres of the circles lie on the same side of the common tangent, then the tangent is called a direct common tangent.
5. 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
• Process:

[Note for teachers : Evaluate if it is possible to construct a direct common tangent without the third circle.]
The teacher can explain the step by step construction of Direct common tangent and with an example

• Developmental Questions:
1. What is a tangent
2. What is a common tangent ?
3. What is a direct common tangent ?
4. What is R and r ?
5. What does the length OA represent here ?
6. Why was a third circle constructed ?
7. Let us try to construct direct common tangent without the third circle and see.
8. What should be the radius of the third circle ?
9. Why was OA bisected and semi circle constructed ?
10. What were OB and OC extended ?
11. What can you say about lines AB and AC ?
12. Name the direct common tangents .
13. At what points is the tangent touching the circles ?
14. Identify the two right angled triangles formed from the figure ? What do you understand ?
• Evaluation:
1. Is the student able to comprehend the sequence of steps in constructing the tangent.
2. Is the student able to identify error areas while constructing ?
3. Is the student observing that the angle between the tangent and radius at the point of intersection is 90º ?
4. 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:
1. What do you think are the applications of tangent constructions ?
2. What is the formula to find the length of direct common tangent ?
3. Can a direct common tangent be drawn to two circles one inside the other ?
4. Observe the point of intersection of extended tangents in relation with the centres of two circles. Infer.
5. What are properties of direct common tangents ?

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## Concept #4. Construction of transverse common tangent.

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# Math Fun

Usage

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