Difference between revisions of "Circles Constructions"
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| Line 152: | Line 152: | ||
*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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|<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 | + | *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 # === | ||
Revision as of 14:47, 2 November 2013
| Philosophy of Mathematics |
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Additional Information
Useful websites
Reference Books
Teaching Outlines
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
- 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
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.
- Students' individual construction materials.
- 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
- 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:
- 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 #
- 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 #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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