Question 69
Let $A, B, C, D$ and $E$ be five points lying in this order on a circle $\Omega$, such that $(C D)$ is parallel to $(B E)$ and $(A B)$ is parallel to $(D E)$. Let $X, Y$ and $Z$ be the midpoints of the segments $[B D],[C E]$ and $[A E]$ respectively.
Prove that the line $(A E)$ is tangent to the circumcircle of $X Y Z$.
Prove that the line $(A E)$ is tangent to the circumcircle of $X Y Z$.