Question

In following figure , AB , a chord of the circle is of length 18 cm. It is perpendicularly bisected at M by PQ. 

Answer 1

Given : AB = 18 cm , MQ = 3 cm

To find : PQ

OQ = OA = r cm (say)

∴ OM = OQ = MQ = (r - 3) cm

AM = MB = 9 cm (PQ ⊥ AB)

In right Δ OMA ,

OM² + MA² = OA²

⇒ (r - 3)² + 9² = r²

⇒ r² - 6r + 9 + 81 = r² 

⇒ 6r = 90

⇒ r = 15 cm

PQ = 2r

(Perpendicular bisector of a chord passes through the centre of the circe)

PQ = 2(15)

PQ = 30 cm