Question 55
In square $ABCD$, points $M,N$ lie in the interiors of sides $BC,CD$ respectively, with $\angle MAN=45^\circ$. Let $O$ be the intersection of the circle through $C,M,N$ with segment $AC$.
a) Prove that $OM=ON$.
b) Prove that $O$ is the center of the circle through $A,M,N$.
a) Prove that $OM=ON$.
b) Prove that $O$ is the center of the circle through $A,M,N$.