1,040
edits
Changes
From Karnataka Open Educational Resources
The longest chord passes through the centre of the circle (view source)
Revision as of 07:14, 4 December 2013
, 07:14, 4 December 2013→Activity No # Construction of Direct common tangent
<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" />
<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:
*Process:
The teacher can explain the step by step construction of Direct common tangent and with an example :
The teacher can explain the step by step construction of Direct common tangent and with an example.
[Note for teachers : Evaluate if it is possible to construct a direct common tangent without the third circle.]
Developmental Questions:
Developmental Questions:
#What is a tangent
#What is a tangent
# Identify the two right angled triangles formed from the figure ? What do you understand ?
# Identify the two right angled triangles formed from the figure ? What do you understand ?
*Evaluation:
*Evaluation:
# 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 ?
