Question

In figure, If OA = 5 cm, AB = 8 cm and OD is perpendicular to chord AB then CD equals –

(a) 2 cm

(b) 3 cm

(c) 4 cm

(d) 5 cm

Answer 1

Answer is (a) 2 cm

radius (OA) = 5 cm

OD ⊥ AB

∴ OC ⊥ AB

Perpendicular drawn from center of circle bisects the chord.

AC = BC = AB

AC = \(\frac { 1 }{ 2 }\) × 8

AC = 4 cm

In right angled triangle OCA

OA² = OC² + AC²

OC² = OA² – AC²

= (5)² – (4)²

= 25 – 16 = 9

OC = \(\sqrt { 9 }\)

OC = 3 cm.

∵ OD = OA = 5 = radius of circle

CD = OD – OC

= 5 – 3

CD = 2 cm