Geometry (Triangles)

Hello all, I have 2 different problems. Someone, please help me in these problems. (1) DABC is right angled at A. D is a point on AB such that CD=1. AE is the altitude from A to BC. If BD=BE=1, then the length of AD equals = ? (2) In DABC, side AB=20, AC=11 & BC=13. The diameter of the semicircle inscribed in ABC, whose diameter lies on AB and that is tangent to AC & BC is. Thanks in advance.

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