SHARYGIN 2019 Problem 7

Let $AH_A, BH_B, CH_C$ be the altitudes of the acute-angled triangle $ABC$. Let $X$ be an arbitrary point of segment $CH_C$, and $P$ be the common point of circles with diameters $H_CX$ and $BC$, distinct from $H_C$. The lines $CP$ and $AH_A$ meet at point $Q$, and the lines $XP$ and $AB$ meet at point $R$. Prove that $A, P, Q, R, H_B$ are concyclic.