MathDB
equilateral wanted, started with intersection of 2 perp. lines with a circle

Source: TOT 426 1994 Autumn A J3 - Tournament of Towns

June 12, 2024
geometryEquilateral

Problem Statement

Two-mutually perpendicular lines \ell and mm intersect each other at a point of the circumference of a circle, dividing it into three arcs. A point MiM_i (i=1i = 1,22,33) is taken on each arc so that the tangent line to the circumference at the point MiM_i intersects \ell and mm in two points at the same distance from MiM_i (that is MiM_i is the midpoint of the segment between them). Prove that the triangle M1M2M3M_1M_2M_3 is equilateral.
(Przhevalsky)