Circles Constructions

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Concept #1. Construction of chord.

Learning objectives

Notes for teachers

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Concept #2. Construction of Tangent.

Learning objectives

Notes for teachers

Activity No #

  • Estimated Time
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  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Concept #3. Construction of direct common tangent.

Learning objectives

Notes for teachers

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

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 ?

Activity No #

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  • Evaluation
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Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Concept #4. Construction of transverse common tangent.

Learning objectives

Notes for teachers

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner

Activity No #

  • Estimated Time
  • Materials/ Resources needed
  • Prerequisites/Instructions, if any
  • Multimedia resources
  • Website interactives/ links/ / Geogebra Applets
  • Process/ Developmental Questions
  • Evaluation
  • Question Corner


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