Let $AC$ be the largest side of the triangle $ABC$. The point M is selected on the ray $AC$ ray, and point $N$ on ray $CA$ such that $CN = CB$ and$ AM = AB$ . a) Prove that $\vartriangle ABC$ is isosceles if we know that $BM = BN$. b) Will the statement remain true if $AC$ is not necessarily the largest side of triangle $ABC$?