In Fig. 10.3, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to:
Fig. 10.3
(A) 2 cm
(B) 3 cm
(C) 4 cm
(D) 5 cm
(A) 2 cm
Solution:
We know that the perpendicular from the centre of a circle to a chord bisects the chord.
Given OA = 5 cm
Using Pythagoras theorem,
(Taking positive square root, because length is always positive)
OA = OD (same because both are radius)
OD = 5 cm
CD = OD – OC = 5 – 3 = 2 cm
Therefore option (A) is correct.