Construction of transverse common tangent

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The transverse common tangents also meet on the line of centres and divide it internally in the ratio of the radii.


To construct transverse common tangents for the given circles.

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.

Materials/ Resources needed

  • Digital: Laptop, geogebra file, projector and a pointer.
  • Non Digital: Students' individual construction materials.
  • Gegebra file:

Process (How to do the activity)

Note: In general,

  1. The two circles are named as C1 and C2
  2. The distance between the centre of two circles is 'd'
  3. Radius of one circle is taken as 'R' and other as 'r'
  4. The length of tangent is 't'

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 ?