Question

AB is a chord of length 8cm in a circle of center O and radius OA=5cm. Radius OD is a line perpendicular to AB, find CD.

Answer 1

Answer:

We know that, the perpendicular from the centre of a circle to a chord bisects the chord.

AC = CB = 1/2 AB = 1/2 x 8 = 4 cm

given OA = 5 cm

AO2 = AC2 + OC2   

(5)2 = (4)2 + OC2

25 = 16 + OC2

OC2 = 25-16 = 9

OC = 3 cm

[taking positive square root, because length is always positive]

OA = OD [same radius of a circle]

OD = 5 cm

CD = OD – OC = 5 – 3 = 2 cm