classical geo given at balkan mo
Source: Balkan Math Olympiad BkMO 2004, problem 3
May 7, 2004
geometryincentercircumcircleBMO
Problem Statement
Let be an interior point of an acute triangle . The circles with centers the midpoints of its sides and passing through mutually intersect the second time at the points , and different from . Prove that is the incenter of the triangle if and only if is the circumcenter of the triangle .