Question 174
In an acute-angled triangle $ABC$, point $O$ is the circumcenter and $H$ the orthocenter. Points $B'$ and $C'$ are the reflections of $B$ in line $AC$ and of $C$ in line $AB$, respectively. Point $K$ is the circumcenter of triangle $HB'C'$, point $D$ the midpoint of $KB$, and $S$ the intersection of line $OD$ with the perpendicular to $AB$ at $A$. Prove that $KA = KS$.