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In two concentric circles, a chord length 80 cm of larger circle becomes a tangent to the smaller circle whose radius is 9 cm. The radius of the larger circle will be

In two concentric circles, a chord length 80 cm of larger circle becomes a tangent to the smaller circle whose radius is 9 cm. The radius of the larger circle will be Correct Answer 41 cm

Given:

Chord of larger circle = Tangent to smaller circle = 80 cm

Radius of smaller circle = 9 cm

Formula:

Pythagorus theorem, H2 = P2 + B2

Calculation:

Radius of smaller circle will bisect the chord as tangent is perpendicular to radius of a circle

Suppose, Radius of larger circle = R,

⇒ R2 = 92 + (80/2)2

⇒ R2 = 81 + 1600 = 1681

⇒ R = 41 cm

∴ Radius of larger circle = 41 cm

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