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Question
Find the length of a chord which is at a distance of 5 cm from the centre of a circle of radius 13 cm.
Solution
Let AB be a chord of a circle with centre O and radius 13 cm. Draw OL ⊥ AB.
Join OA. Clearly, OL = 5 cm and OA = 13 cm.
In the right triangle OLA, we have
OA2 = OL2 + AL2
⇒ 132 = 52 + AL2
⇒ AL2 = 144 cm2
⇒ AL = 12 cm
Since, the perpendicular from centre to the chord bisects the chord. Therefore,
AB = 2AL = 2 x 12 cm = 24 cm.
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