DE-BUNDESWETTBEWERB 2022 Problem 7

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: $\angle ACM_c = \angle KCB$ .