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Two concentric circles with centre O, the radius of the inner circle is 8 cm and a chord AB of length 30 cm is tangent to the inner circle, Find the area of which is not common to both the circles?

Two concentric circles with centre O, the radius of the inner circle is 8 cm and a chord AB of length 30 cm is tangent to the inner circle, Find the area of which is not common to both the circles? Correct Answer 225π

Given:

Radius of inner circle = 8 cm

Chord of bigger circle = 30 cm

Concept:

Radius drawn on the tangent is perpendicular on the tangent. The radius will divide the chord in two equal half. Thus, by using Pythagorean triplets, calculate the area of the bigger circle. The area outside the inner circle is the area which is not common to both the circles.

Formula used:

In right angled triangle;

H2 = P2 + B2

Area between two concentric circle = π(R2 – r2)

Where,

H → Hypotenuse

P → Perpendicular

B → Base

R → Radius of outer circle

r → Radius of inner circle

Calculation:

= π × 25 × 9

= 225π 

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