A convex quadrilateral $ABCD$ is given in which the bisectors of the interior angles $\angle ABC$ and $\angle ADC$ have a common point on the diagonal $AC$. Prove that the bisectors of the interior angles $\angle BAD$ and $\angle BCD$ have a common point on the diagonal $BD$.
Problem
Source: 2020 1st Memorial Mathematical Contest "Aleksandar Blazhevski-Cane" p1
Tags: geometry, concurrency, concurrent