HSCE SET : B 11. In the given figure, O is the centre of the circle and OC I AB. If AB = 12 cm and PC = 2 cm, find the radius of the circle. O P A B hings С (A) 10 cm (B) 16 cm (C) None of these (D) 5 cm atures I things
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(D) 5 cm atures I things
Let the radius of the circle be r. .. OB = OC = r and OA = AC + OC = (7.5 +
r) cm
AABO is a right angled triangle (since AB is a tangent). By Pythagoras theorem, OA² = AB² + OB²
(7.5+r)² = 15² +r²
→ 56.25 + 15r+r² = 225 +r²
→ 15r = 225 - 56.25 = 168.75
⇒ r = 11.25 cm
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