Find the diameter of the semicircle inscribed in ABC, whose diameter lies on AB, and that is tangent to AC and BC.

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In triangleABC, side AB = 20, AC = 11, and BC = 13. Find the diameter of the semicircle inscribed in ABC, whose diameter lies on AB, and that is tangent to AC and BC.

Triangle ABC is inscribed in a circle. Construct chord AD and let E be the intersection of chords AD and BC. If AB = AC = 12 and AE = 8, then what is the length of AD?