Question

A chord is at a distance of 8 cm from the centre of a circle of radius 17 cm. The length of the chord is
(a) 25 cm
(b) 12.5 cm
(c) 30 cm
(d) 9 cm

Answer 1

(c) 30 cm

Let AB be the chord of the given circle with centre O and a radius of 17 cm.
From O, draw OM perpendicular to AB.
Then OM = 8 cm and OB = 17 cm

From the right ΔOMB, we have:
OB² = OM² + MB²
⇒ 17² = 8² + MB²
⇒ 289 = 64 + MB²
⇒ MB² = (289 - 64) = 225
⇒ $\mathrm{MB}=\sqrt{225}\mathrm{cm}=15\mathrm{cm}$
The perpendicular from the centre of a circle to a chord bisects the chord.
∴ AB = 2 × MB = (2 x 15) cm = 30 cm
Hence, the required length of the chord is 30 cm.