Question 40
Let $ABCC_1B_1A_1$ be a convex hexagon such that $AB = BC$, and the perpendicular bisectors of the segments $\overline{AA_1}, \overline{BB_1}$ and $\overline{CC_1}$ coincide. Let the diagonals $AC_1$ and $A_1C$ meet at the point $D$, and denote the circumcircle of triangle $ABC$ by $\omega$. Let $\omega$ and the circumcircle of triangle $A_1BC_1$ meet again at a point $E \neq B$.
Prove that the intersection point of the lines $BB_1$ and $DE$ lies on $\omega$.
Prove that the intersection point of the lines $BB_1$ and $DE$ lies on $\omega$.