Question

Find the length of chord of a circle which is a distance of 5cm fromthe centre of the circle the radius of the circle is 13cm

Answer 1

Let the AB be the chord of the circle of length x

The centre of the circle is O and the point at which perpendicular meets the chord is P such that P is the mid - point of the AB.

In tri. OPA

${oa}^{2} = {op}^{2} + {pa}^{2} \\ {13}^{2} = {5}^{2} + {pa}^{2} \\ pa = \sqrt{ {13}^{2} - {5}^{2} } \\ pa = \sqrt{144} = 12$

Length of the chord =2 PA =2*12=24 cm.

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