\(ABCD\) 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.