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.
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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
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