Quadrant of a circle

Geometry Level 3

Circle β \beta with center at M M is inscribed in a quadrant of a circle as shown. If the area of the shaded region is 25 4 2 π − 25 2 \dfrac{25}{4}\sqrt{2}\pi-\dfrac{25}{2} , find the radius of the inscribed circle. If your answer is r r , give r 2 + r 3 r^2+r^3 .


The answer is 150.

A Former Brilliant Member by A Former Brilliant Member

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