Question

In the given figure, O is the centre of the circle. AB and CD are two chords of the circle. OM is perpendicular to AB and ON is perpendicular to CD. AB = 24 cm, OM = 5 cm, ON = 12 cm. Find the:

1. radius of the circle.
2. length of chord CD.

Answer 1

AB = 24 cm, OM = 5 cm, ON = 12 cm.

i. In ΔAOM,

OA² = OM² + AM²

OA² = 5² + 12²   

OA² = 25 + 144 = 169

OA = 13 cm

Thus, radius of the circle is 13 cm.

ii. In ΔCON,

OC² = ON² + CN²

13² = 12² + CN²   ...(∵ OC = OA = 13 (Radius))

169 – 144 = CN²

CN² = 25

CN = 5

Thus length of chord CD = 2CN = 2 × 5 = 10 cm.