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Question

O is centre of the circle. Find the length of radius, if the chord of length 24 cm is at a distance of 9 cm from the centre of the circle.

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Solution

Join OA.

Let the perpendicular drawn from point O to the chord AB be P.
We know that the perpendicular drawn from the centre of the circle to the chord bisects the chord.
So, AP=AB2=242=12 cm
In OPA,
We apply the Pythagoras theorem,
OP2+AP2=OA292+122=OA2OA2=81+144=225OA=225=15 cm
Hence, the radius of the circle is 15 cm.

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