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Question
In the following figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to ______.
Options
2 cm
3 cm
4 cm
5 cm
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Solution
In the following figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to 2 cm.
Explanation:
We know that, the perpendicular from the centre of a circle to a chord bisects the chord.
AC = CB = `1/2` AB = `1/2` × 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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