Question 161
A triangle $ABC$ with $AB = AC$ is obtuse at $A$. Let $M$ be the mirror image of $A$ across $C$. The perpendicular bisector of the line segment $AM$ meets the line $AB$ at point $P$. Given that lines $PM$ and $BC$ are perpendicular, prove that $APM$ is an equilateral triangle.
Marcel Neferu
Marcel Neferu