Question 73
Let $c(O,R)$ be a circle, $AB$ a diameter and $\Gamma$ the midpoint of the arch $\widehat{AB}$. We draw the circle $c_I(K,KO)$, where $K$ is a point of the segment $OA$ and we consider the tangents $\Gamma\Delta$, $\Gamma O$ from $\Gamma$ to the circle $c_I(K,KO)$. The line $K\Delta$ intersects the circle $c(O,R)$ at the points $E$ and $Z$ (the point $E$ lies in the same semicircle with $\Gamma$). Finally, the lines $E\Gamma$ and $\Gamma Z$ intersect $AB$ at the points $N$ and $M$, respectively. Prove that the quadrilateral $EMZN$ is an isosceles trapezium inscribed in a circle whose center lies on the circle $c(O,R)$.