Question 3
Let $P_1,P_2,P_3,P_4$ be four points on a circle. Let $I_1$ be the incentre of $P_2P_3P_4$, $I_2$ the incentre of $P_1P_3P_4$, $I_3$ the incentre of $P_1P_2P_4$, and $I_4$ the incentre of $P_1P_2P_3$. Prove that $I_1,I_2,I_3,I_4$ are the vertices of a rectangle.
