MathNet 2018-part-06 — 181 problems (EN–VI) Question 95

There is isosceles obtuse triangle $ABC$ with vertex in point $B$ given. Perpendicular bisector to side $BC$ intersects lines $AC$ and $AB$ in points $K$ and $M$ respectively. Prove, that point, symmetric to point $A$ with respect to line $BK$, is on line $CM$.

(Anton Trigub)