Difference between revisions of "Construction of transverse common tangent"
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m (Preeta moved page Circles and lines activity 5 to Construction of transverse common tangent without leaving a redirect) |
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| − | + | ===Objectives=== | |
| − | = | + | ===Estimated Time=== |
| + | 45 minutes | ||
| − | = | + | ===Prerequisites/Instructions, prior preparations, if any=== |
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| − | ==Prerequisites/Instructions, if any== | ||
# The students should have prior knowledge of a circle , tangent and direct and transverse common tangents . | # The students should have prior knowledge of a circle , tangent and direct and transverse common tangents . | ||
# They should understand that a tangent is always perpendicular to the radius of the circle. | # They should understand that a tangent is always perpendicular to the radius of the circle. | ||
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* Radius of one circle is taken as 'R' and other as 'r' | * Radius of one circle is taken as 'R' and other as 'r' | ||
* The length of tangent is 't' | * The length of tangent is 't' | ||
| − | == | + | ===Materials/ Resources needed=== |
| − | Laptop | + | * Laptop, geogebra file, projector and a pointer. |
| − | + | * Students' individual construction materials. | |
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| − | ==Process (How to do the activity)== | + | ===Process (How to do the activity)=== |
| − | + | The teacher can explain the step by step construction of Transverse common tangent. | |
| − | + | * __FORCETOC__ Developmental Questions (What discussion questions) | |
# What is a transverse common tangent ? | # What is a transverse common tangent ? | ||
# What is the radius of the third circle ? | # What is the radius of the third circle ? | ||
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# Name the transverse common tangents . | # Name the transverse common tangents . | ||
# At what points is the tangent touching the circles ? | # At what points is the tangent touching the circles ? | ||
| − | + | * Evaluation (Questions for assessment of the child) | |
# Is the student able to comprehend the sequence of steps in constructing the tangent. | # 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 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 observing that the angle between the tangent and radius at the point of intersection is 90º ? | ||
# Is the student able to understand the difference in the construction protocol between direct common tangent and transverse common tangent ? | # Is the student able to understand the difference in the construction protocol between direct common tangent and transverse common tangent ? | ||
| − | + | * Question Corner | |
# What is the formula to find the length of transverse common tangent ? | # What is the formula to find the length of transverse common tangent ? | ||
# Can a direct common tangent be drawn to two circles one inside the other ? | # Can a direct common tangent be drawn to two circles one inside the other ? | ||
# What are properties of transverse common tangents ? | # What are properties of transverse common tangents ? | ||
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Revision as of 06:53, 8 May 2019
Objectives
Estimated Time
45 minutes
Prerequisites/Instructions, prior preparations, if any
- The students should have prior knowledge of a circle , tangent and direct and transverse common tangents .
- 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 opposite side of the common tangent, then the tangent is called a transverse 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'
Materials/ Resources needed
- Laptop, geogebra file, projector and a pointer.
- Students' individual construction materials.
Process (How to do the activity)
The teacher can explain the step by step construction of Transverse common tangent.
- Developmental Questions (What discussion questions)
- What is a transverse common tangent ?
- What is the radius of the third circle ?
- What is the difference in finding the radius of the third circle in constructing Dct and that of Tct ?
- Why was a third circle constructed ?
- Let us try to construct transverse common tangent without the third circle and see.
- Name the transverse common tangents .
- At what points is the tangent touching the circles ?
- Evaluation (Questions for assessment of the child)
- 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 understand the difference in the construction protocol between direct common tangent and transverse common tangent ?
- Question Corner
- What is the formula to find the length of transverse common tangent ?
- Can a direct common tangent be drawn to two circles one inside the other ?
- What are properties of transverse common tangents ?