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Question

Question 2
In figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to


(A) 2 cm
(B) 3 cm
(C) 4 cm
(D) 5 cm


Solution

The answer is (A).
We know that, the perpendicular from the centre of a circle to a chord bisects the chord.
AC=CB=12AB=12×8=4 cmgiven, OA=5 cmAO2=AC2+OC2(5)2=(4)2+OC225=16+OC2OC2=2516=9OC=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

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