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Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle.

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Out of the two concentric circles, the radius of the outer circle is 5 cm and the chord AC of length 8 cm is a tangent to the inner circle. Find the radius of the inner circle.

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From the figure,

Chord AB = 8 cm

OC is perpendicular to the chord AB

AC = CB = 4 cm

In right triangle OCA

OC2 + CA2 = OA2

OC2 = 52 – 42 = 25 – 16 = 9

OC = 3 cm

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