# Circle Inscribed in a Trapezium

Geometry Level 3

$$ABCD$$ is a trapezium with $$AB < CD$$ and $$AB$$ parallel to $$CD$$. $$\Gamma$$ is a circle inscribed in $$ABCD$$, such that $$\Gamma$$ is tangent to all four sides. If $$AD = BC = 25$$ and the area of $$ABCD$$ is $$600$$, what is the radius of $$\Gamma$$?

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