OME 1987 Problem 1

Let $a, b, c$ be the side lengths of a scalene triangle and let $O_a, O_b$ and $O_c$ be three concentric circles with radii $a, b$ and $c$ respectively. (a) How many equilateral triangles with different areas can be constructed such that the lines containing the sides are tangent to the circles? (b) Find the possible areas of such triangles.