Not as They Seem to Be

Geometry Level 4

Triangle ABCABC is isosceles, with AB=ACAB=AC and altitude AM=11.AM=11. Suppose that there is a point DD on AM\overline{AM} with AD=10AD=10 and BDC=3BAC.\angle BDC=3\angle BAC. Then the perimeter of ABC\triangle ABC may be written in the form a+b,a+\sqrt{b}, where aa and bb are integers. Find a+b.a+b.

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