Let $ABC$ a triangle with $AB<AC$ and let $I$ it´s incenter. Let $\Gamma$ the circumcircle of $\triangle BIC$. $AI$ intersect $\Gamma$ again in $P$. Let $Q$ a point in side $AC$ such that $AB=AQ$ and let $R$ a point in $AB$ with $B$ between $A$ and $R$ such that $AR=AC$. Prove that $IQPR$ is cyclic.
Problem
Source: Mathematics Regional Olympiad of Mexico Southeast 2020 P2
Tags: geometry, incenter, circumcircle, cyclic quadrilateral