A chord is at a distance of 8 cm from the centre of a circle of radius 17 cm. The length of the chord is

(a) 25 cm

(b) 12.5 cm

(c) 30 cm

(d) 9 cm

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Solution

let, the chord intersects the circle at A & B.

O be the center of the circle.

Draw a perpendicular form center O i.e. OD

Join OB & OA

In tri ODA,

L ODA = 90

By Pythagoras theorem

OB²=OD²+DB²

17²=OD²+8²

OD=15

Length of chord=OA+OD=2OA=2 x 15=30cm
Hence, option c is correct

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