Question 22
Let $AB\Gamma\Delta$ be a quadrilateral inscribed in a circle with centre $O$. The line perpendicular to the side $B\Gamma$ at its midpoint $E$ meets the line $AB$ at point $Z$. The circumcircle of the triangle $\Gamma EZ$ intersects the side $AB$ for a second time at point $H$ and the line $\Gamma\Delta$ at point $\Theta \neq \Delta$. The line $E\Theta$ meets the line $A\Delta$ at point $K$ and the line $\Gamma H$ at point $\Lambda$. Prove that the points $A$, $H$, $\Lambda$, $K$ are concyclic.