MathDB
equilateral with vertices on 3 concentric circles, radii sidelengths of scalene

Source: Spanish Mathematical Olympiad 1987 P1

August 2, 2018
geometryconcentric circlesEquilateral Triangle

Problem Statement

Let a,b,ca, b, c be the side lengths of a scalene triangle and let Oa,ObO_a, O_b and OcO_c be three concentric circles with radii a,ba, b and cc 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.
Back to ProblemsView on AoPS