Problem

Source: German Bundeswettbewerb 2022, Round 2, Problem 3

Tags: geometry, perpendicular bisector



In an acute triangle $ABC$ with $AC<BC$, lines $m_a$ and $m_b$ are the perpendicular bisectors of sides $BC$ and $AC$, respectively. Further, let $M_c$ be the midpoint of side $AB$. The Median $CM_c$ intersects $m_a$ in point $S_a$ and $m_b$ in point $S_b$; the lines $AS_b$ und $BS_a$ intersect in point $K$. Prove: $\angle ACM_c = \angle KCB$.