| Line 66: |
Line 66: |
| | #Activity #1 - [[Circles_and_lines_activity_3|Understanding secant and tangent using Geogebra]] | | #Activity #1 - [[Circles_and_lines_activity_3|Understanding secant and tangent using Geogebra]] |
| | | | |
| − | ==Concept # Construction of tangents== | + | ==Concept #3 Construction of tangents== |
| | ===Learning objectives=== | | ===Learning objectives=== |
| | # The students should know that tangent is a straight line touching the circle at one and only point. | | # The students should know that tangent is a straight line touching the circle at one and only point. |
| Line 78: |
Line 78: |
| | | | |
| | ===Notes for teachers=== | | ===Notes for teachers=== |
| − | ===Activity No # 1. Construction of Direct common tangent === | + | ===Activities=== |
| − | {| style="height:10px; float:right; align:center;"
| + | #Activity #1 - Construction of Direct common tangent |
| − | |<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;">
| + | #Activity #2 - Construction of Transverse common tangent=== |
| − | ''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div>
| |
| − | |}
| |
| − | *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 : This geogebra file was created by Mallikarjun sudi of Yadgir.
| |
| − | <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:
| |
| − | The teacher can explain the step by step construction of Direct common tangent and with an example.<br>
| |
| − | 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 ?
| |
| − | # [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.
| |
| − | | |
| − | <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" />
| |
| − | | |
| − | ===Activity No # 2. Construction of Transverse common tangent===
| |
| | {| style="height:10px; float:right; align:center;" | | {| style="height:10px; float:right; align:center;" |
| | |<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;"> |
