Three Circles

Geometry Level 3

Circles A A , B B , and C C are shown above. The difference between the lengths of major arc C B CB and minor arc C B CB is 8 π 3 \dfrac {8π} {3} . What is the area of △ A B C \triangle ABC ?

√ 3 4 \frac {√3} {4} 4 π 3 \frac {4π} {3} 3 \sqrt3 3 2 \frac {\sqrt3} {2} 4 π 2 3 9 \frac {4π^2\sqrt3} {9}

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A A by a a , 25, USA

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1 solution

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Aug 19, 2015

It Is very easy to get the radious of one of each circle: R = 8 × π 3 ∗ 3 2 2 × π = 2 R=\frac{\frac{8 \times \pi}{3}*\frac{3}{2}}{2 \times \pi} = 2 So we get the area of the triangles is: S A B C = 3 S_{ABC} = \sqrt{3}

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