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

(第十三届AIME1995 第9题)