Construction of transverse common tangent

Estimated Time
45 minutes

Prerequisites/Instructions, prior preparations, if any

 * 1) The students should have prior knowledge of a circle, tangent and direct and transverse common tangents.
 * 2) They should understand that a tangent is always perpendicular to the radius of the circle.
 * 3) They should know construction of a tangent to a given point.
 * 4) If the same straight line is a tangent to two or more circles, then it is called a common tangent.
 * 5) If the centres of the circles lie on opposite side of the common tangent, then the tangent is called a transverse common tangent.
 * 6) 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)
 * 1) What is a transverse common tangent ?
 * 2) What is the radius of the third circle ?
 * 3) What is the difference in finding the radius of the third circle in constructing Dct and that of Tct ?
 * 4) Why was a third circle constructed ?
 * 5) Let us try to construct transverse common tangent without the third circle and see.
 * 6) Name the transverse common tangents.
 * 7) At what points is the tangent touching the circles ?
 * Evaluation (Questions for assessment of the child)
 * 1) Is the student able to comprehend the sequence of steps in constructing the tangent.
 * 2) Is the student able to identify error areas while constructing ?
 * 3) Is the student observing that the angle between the tangent and radius at the point of intersection is 90º ?
 * 4) Is the student able to understand the difference in the construction protocol between direct common tangent and transverse common tangent ?
 * Question Corner
 * 1) What is the formula to find the length of transverse common tangent ?
 * 2) Can a direct common tangent be drawn to two circles one inside the other ?
 * 3) What are properties of transverse common tangents ?