Question 101
The excircles of $\triangle ABC$ touch the sides $AB$, $BC$ and $CA$ at points $M$, $N$ and $P$, respectively. Let $I$ and $O$ be the incenter and the circumcenter of $\triangle ABC$. Prove that if $AMNP$ is a cyclic quadrilateral, then:
a) the points $M$, $P$ and $I$ are collinear;
b) the points $I$, $O$ and $N$ are collinear.
a) the points $M$, $P$ and $I$ are collinear;
b) the points $I$, $O$ and $N$ are collinear.