Problem

Source: Romania TST 2015 Day 4 Problem 1

Tags: equal angles, perimeter, Romanian TST, geometry



Let $ABC$ and $ABD$ be coplanar triangles with equal perimeters. The lines of support of the internal bisectrices of the angles $CAD$ and $CBD$ meet at $P$. Show that the angles $APC$ and $BPD$ are congruent.