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Two concentric circles are of radii 6.5 cm and 2.5 cm. Find the length of the chord of the larger circle which touches the smaller circle.

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Let O be the center of circle. Draw two concentric circles are of radii 6.5 cm and 2.5 cm, and

AB = Chord of the larger circle which touches the smaller circle at C.

From Figure:

OC = radius = 2.5 cm

OA = 6.5 cm

AC = CB

OC ⊥ AB and OC bisects AB at C.

In right ∆OPT,

By Pythagoras Theorem:

OA2 = OC2 + AC2

6.52 = 2.52 + AC2

42.25 = 6.25 + AC2

AC = 6

Length of chord of a circle = AB = 2 x AC = 2 x 6 = 12 cm.

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