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Two concentric circles are drawn with radii 12 cm. and 13 cm. What will be the length of any chord of the larger circle that is tangent to the smaller circle.

Two concentric circles are drawn with radii 12 cm. and 13 cm. What will be the length of any chord of the larger circle that is tangent to the smaller circle. Correct Answer 10 cm.

Given

Two concentric circles are drawn with radii 12 cm and 13 cm.

Calculation

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Let O be the center of the circle and OC and OB the radius of two circles.

AB is the chord for the bigger circle and tangent for the smaller circle.

OC is perpendicular to AB

In Δ OCB

OB2 = OC2 + BC2

132 - 122 = BC2

BC2 = 25

BC = 5

AB = 2 × 5

AB = 10 cm.

 

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