Question 44
A point $X$ is chosen on the median $AD$ of triangle $ABC$. The circumcircle of triangle $ABX$ intersects the median $BE$ of triangle $ABC$ at point $Y \neq B$. The circumcircle of triangle $EXY$ intersects the line $DE$ at point $K \neq E$. Prove that the location of $K$ does not depend on $X$.