Difference between revisions of "Construction of transverse common tangent"
Jump to navigation
Jump to search
(Created page with "{{subst:Math-Activity}}") |
|||
| Line 1: | Line 1: | ||
__FORCETOC__ | __FORCETOC__ | ||
| − | =Activity No # 1 - | + | =Activity No # 1 - Transverse Common Tangent= |
==Estimated Time== | ==Estimated Time== | ||
| − | + | 45 minutes | |
==Materials/ Resources needed== | ==Materials/ Resources needed== | ||
| + | # Laptop, geogebra file, projector and a pointer. | ||
| + | # Students' individual construction materials. | ||
==Prerequisites/Instructions, if any== | ==Prerequisites/Instructions, 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' | ||
==Multimedia resources== | ==Multimedia resources== | ||
| + | Laptop | ||
==Website interactives/ links/ simulations/ Geogebra Applets== | ==Website interactives/ links/ simulations/ Geogebra Applets== | ||
| + | <ggb_applet width="1280" height="600" version="4.0" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="false" showToolBar="false" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" /> | ||
| + | |||
==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. | ||
==Developmental Questions (What discussion questions)== | ==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)== | ==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== | ==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 ? | ||
| + | |||
==Activity Keywords== | ==Activity Keywords== | ||
| + | #Geogebra | ||
| + | #Transverse common tangent | ||
| − | + | [http://karnatakaeducation.org.in/KOER/en/index.php/Circles_and_lines Back] | |
| − | |||
| − | [http://karnatakaeducation.org.in/KOER/en/index.php/ | ||
Revision as of 02:29, 10 July 2014
Activity No # 1 - Transverse Common Tangent
Estimated Time
45 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 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'
Multimedia resources
Laptop
Website interactives/ links/ simulations/ Geogebra Applets
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 ?
Activity Keywords
- Geogebra
- Transverse common tangent