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− | __FORCETOC__
| + | The direct common tangents to two circles meet on the line of centres and divide it externally in the ratio of the radii. |
− | =Activity No # 1 - '''Name of Activity'''=
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− | ==Estimated Time== | + | === Objectives === |
| + | To construct direct common tangent for the given circle. |
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− | ==Materials/ Resources needed== | + | ===Estimated Time=== |
− | ==Prerequisites/Instructions, if any==
| + | 90 minutes |
− | ==Multimedia resources==
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− | ==Website interactives/ links/ simulations==
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− | ==Process (How to do the activity)==
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− | ==Developmental Questions (What discussion questions)==
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− | ==Evaluation (Questions for assessment of the child)==
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− | ==Question Corner==
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− | ==Activity Keywords==
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− | '''To link back to the concept page''' | + | ===Prerequisites/Instructions, prior preparations, if any=== |
− | <nowiki>
| + | # The students should have prior knowledge of a circle , tangent and the limiting case of a secant as a tangent. |
− | [http://karnatakaeducation.org.in/KOER/en/index.php/'''Give the link of the page name from where activity was given''' Back]
| + | # 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. |
| + | ===Materials/ Resources needed=== |
| + | * Digital: Laptop, geogebra file, projector and a pointer. |
| + | * Non digital: Students' individual construction materials. |
| + | * Geogebra file: This geogebra file was created by Mallikarjun sudi of Yadgir. |
| + | {{Geogebra|zdybngmt}} |
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| + | ===Process (How to do the activity)=== |
| + | Note: In general, |
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| + | The two circles are named as C1 and C2 |
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| + | The distance between the centre of two circles is 'd' |
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| + | Radius of one circle is taken as 'R' and other as 'r' |
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| + | The length of tangent is 't' |
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| + | The teacher can explain the step by step construction of Direct common tangent and with an example. |
| + | * Developmental Questions (What discussion 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 Questions |
| + | # 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 ? |
| + | # [Note for teachers : Evaluate if it is possible to construct a direct common tangent without the third circle.] Examine with the help of following geogebra file made by Ranjani.__FORCETOC__ |
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| + | [[Category:Circles]] |