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Question

In the given figure, O is the centre of two concentric circles of radii 6 cm and 10 cm. AB is a chord of outer circle which touches the inner circle. The length of chord AB is

(a) 8 cm (b) 14 cm (c) 16 cm (d) 136 cm

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Solution

Let the two concentric circles with centre O.

AB be the chord of the larger circle which touches the smaller circle at point P.

∴ AB is tangent to the smaller circle to the point P.

OPAB

By Pythagoras theorem in ΔOPA,

OA2=AP2+OP2

102=AP2+62

AP2=10036=64

AP=8

In ΔOPA,

Since OPAB,

AP = PB (∵ Perpendicular from the centre of the circle bisects the chord)

AB=2AP=2×8=16 cm

∴ The length of the chord of the larger circle is 16 cm.


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