Kaui's trapezium

Geometry Level 4

ABCDABCD is a trapezium with parallel sides ABAB and CDCD. Γ\Gamma is an inscribed circle of ABCDABCD, and tangential to sides AB,BC,CDAB, BC, CD and ADAD at the points E,F,GE, F, G and HH respectively. If AE=2,BE=3,AE=2, BE=3, and the radius of Γ\Gamma is 1212, what is the length of CDCD?

This problem is posed by Kuai Y.

Details and assumptions

A trapezium has a pair of parallel sides.

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