Question 22
Let $A B \Gamma$ be an isosceles acute angled triangle with $AB = A\Gamma$. Let $\Gamma\Delta$ be an altitude of the triangle. The circle $c_2(\Gamma, \Gamma\Delta)$ intersects $A\Gamma$ at point $K$, the extension of $A\Gamma$ at point $Z$ and the circle $c_1(B, B\Delta)$ at point $E$. Finally, $\Delta Z$ intersects the circle $c_1$ at point $M$. Prove that
a. $Z\hat{\Delta}E = 45^\circ$
b. The points $E$, $M$, and $K$ are collinear.
c. The line $BM$ is parallel to the line $E\Gamma$.
a. $Z\hat{\Delta}E = 45^\circ$
b. The points $E$, $M$, and $K$ are collinear.
c. The line $BM$ is parallel to the line $E\Gamma$.