Question 1
Call triangle $ABC$ great if for every point $D$ on side $BC$, with $P,Q$ the perpendicular feet from $D$ to lines $AB,AC$, the reflection of $D$ in line $PQ$ lies on the circumcircle of $ABC$.
Prove that $ABC$ is great if and only if $\angle A=90^\circ$ and $AB=AC$.
General illustrative configuration (new):
Prove that $ABC$ is great if and only if $\angle A=90^\circ$ and $AB=AC$.
General illustrative configuration (new):