The story of the green square.

Geometry Level 3

The green square in the diagram is symmetrically placed at the center of the circle. Four red equilateral triangles are drawn such that square A B C D ABCD is formed. Let y , b , g , y,b,g, and r r be the areas of the yellow, blue, green, and red regions, respectively.

If r = 4 3 r=4\sqrt{3} , find y + g − b y+g-b .

π ( 2 3 + 2 ) − 4 3 \pi\big(2\sqrt{3}+2\big)-4\sqrt{3} 8 + 4 3 + π ( 2 3 + 2 ) 2 8+4\sqrt{3}+\pi\big(2\sqrt{3}+2\big)^2 π 4 ( 16 + 8 3 ) − 8 + 4 3 \dfrac{\pi}{4}\big(16+8\sqrt{3}\big)-8+4\sqrt{3} 4 π + 2 π 3 − 8 − 4 3 4\pi+2\pi\sqrt{3}-8-4\sqrt{3}

A Former Brilliant Member by A Former Brilliant Member

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