# Concentric Circle & Square

Geometry Level 3

Square $$ABCD$$ and circle $$\Gamma$$ have equal areas and share the same center $$O$$. The circle intersects side $$AB$$ at points $$E$$ and $$F$$. Given that $$EF = \sqrt{1600 - 400\pi}$$, what is the radius of $$\Gamma$$?

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