# Kaui's trapezium

Geometry Level 4

$$ABCD$$ is a trapezium with parallel sides $$AB$$ and $$CD$$. $$\Gamma$$ is an inscribed circle of $$ABCD$$, and tangential to sides $$AB, BC, CD$$ and $$AD$$ at the points $$E, F, G$$ and $$H$$ respectively. If $$AE=2, BE=3,$$ and the radius of $$\Gamma$$ is $$12$$, what is the length of $$CD$$?

This problem is posed by Kuai Y.

Details and assumptions

A trapezium has a pair of parallel sides.

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