Three circles tangent to each other.

Geometry Level 2

Three circles of equal radii are tangent to each other as shown in the above figure. The radius of each circle is 5 5 . What is the area of the blue region?

10 ( 2 − π 2 ) 10(\sqrt{2}-\frac{\pi}{2}) 25 ( 3 − π 4 ) 25(\sqrt{3}-\frac{\pi}{4}) 25 ( 3 − π 2 ) 25(\sqrt{3}-\frac{\pi}{2}) 10 ( 3 − π 2 ) 10(\sqrt{3}-\frac{\pi}{2}) 100 ( 3 − π 2 ) 100(\sqrt{3}-\frac{\pi}{2})

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Hana Wehbi
Jul 30, 2018

The area of the blue region is the area of the equilateral triangle minus the three sectors of angle 6 0 ∘ 60 ^\circ = 100 3 4 − 25 π 2 = 25 ( 3 − π 2 ) . \large\frac{100\sqrt{3}}{4}- \frac{25\pi}{2} = 25(\sqrt{3}-\frac{\pi}{2}).

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