angle MBC is equal to angle FC iff ABC is equilateral
Source: Moldova TST 2005 for JBMO, day 2, problem 1
April 11, 2005
trigonometrygeometrycircumcircleangle bisectortrig identitiesLaw of Sinesperpendicular bisector
Problem Statement
Let be an acute-angled triangle, and let be the foot of its altitude from the vertex . Let be the midpoint of the segment . Assume that . Then the angle is equal to angle if and only if the triangle is equilateral.