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Ex 11.2, 5

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

The tangents can be constructed on the given circles as follows.

  1. Draw a line segment AB of 8 cm. Taking A and B as centre, draw two circles of 4 cm and 3 cm radius.
  2. Bisect the line AB. Let the mid-point of AB be C.
  3. Taking C as centre, AC as radius, draw a circle which intersects the circles at points P, Q, R, and S.
  4. Join BP, BQ, AS, and AR.

These are the required tangents.


We need to prove

  • BP and BQ are tangents to larger circle.
  • AS and AR are tangents to smaller circle.
  • Join BS and BR.

∠ASB is an angle in the semi-circle of the blue circle


And we know that angle in a  semi-circle is a right angle.

∴ ∠ASB = 90°

⇒ AS ⊥ BS

Since BS is the radius of the circle,

AS has to be a tangent of the circle.

Similarly, AR, BP, BQ are tangents.


  1. Chapter 11 Class 10 Constructions
  2. Concept wise
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CA Maninder Singh
CA Maninder Singh is a Chartered Accountant for the past 7 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .