# Concentric circles and equilateral triangle

Geometry Level 5

Three concentric circles each have radii $$8\text{ cm}, 15\text{ cm}, 17\text{ cm}.$$

If the largest possible area of the equilateral triangle with one vertex on each circle is of the form $$\left(a+b\dfrac{\sqrt{3}}{4}\right) \text{cm}^2,$$ where $$a$$ and $$b$$ are positive integers, find $$a+b.$$

×