Question

A chord of 24 cm length is drawn in a  circle of radius 13 cm. The distance of chord from center of circle is –

(a) 12 cm

(b) 5 cm

(c) 6.5 cm

(d) 12 cm

Answer 1

Answer is (b) 5 cm

AM = BM = \(\frac { 1 }{ 2 }\) × AM = \(\frac { 1 }{ 2 }\) × 24 = 12 cm

In right ∆OAM

OA² = AM² + OM²

(13)² = (12)² + (OM)²

OM² = (13)² – (12)² = 169 – 144

OM² = 25

OM = \(\sqrt { 25 }\) = 5 cm

Thus, distance of chord from center of circle = 5 cm.