Question 2
Let $ABCD$ be a rectangle, $E$ is a point on the line segment $BC$. The circle $\omega$ has center $A$ and passes through $E$. Extension lines $EB$ and $AE$ meet $\omega$ at $X$ and $Y$, respectively, as shown in the diagram below. Prove that $DC$ is tangent to the circle passing through $Y$, $X$ and $D$.
Paper instruction: Give a full solution, subject to the example-or-proof instructions in the question.
Paper instruction: Give a full solution, subject to the example-or-proof instructions in the question.