# Perplexing Pizza Crust

Geometry Level 5

A square box $$ABCD$$ of side length $$100$$ contains a slice of pizza. The box meets with an inscribed circle at points of tangency $$H$$, $$I$$, $$J$$, $$K$$, and there is an inscribed circle quadrant with centre $$D$$.

Let $$L$$ be the point where arc $$AC$$ intersects the line $$DH$$, and $$M$$ be the point where the same arc intersects the line $$DI$$. Find the area of the pizza crust (the shaded region $$HIML$$) to the nearest integer.

Details and Assumptions:

• Use the approximation $$\tan ^{ -1 }{ (\frac{1}{2}) } =0.464$$.

• Use the approximation $$\pi = 3.142$$.

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