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Question

In the given figure PQ is the diameter of a circle with centre O, and is perpendicular to the chord AB. If AB = 8cm and QM = 2cm, find the radius of the circle.


  1. 5 cm

  2. 6 cm

  3. 2 cm

  4. 4 cm


Solution

The correct option is A

5 cm


OM is perpendicular to AB  [perpendicular from the centre of the circle bisects the chord.]

AM=MB=4cm

Let radius of the circle OA be r cm.

OM = OQ - MQ    ( r - 2) cm

Using Pythagoras theorem in right angled triangle OAM

OA2=MA2+OM2

   r2=42+(r2)2

  r2=16+r24r+4

   r=5cm

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