Problem

Source: Iran MO 2023 3rd round , Day 2 P3

Tags: geometry



In the acute triangle $\triangle ABC$ , $H$ is the orthocenter. $S$ is a point on $(AHC)$ st $\angle ASB = 90$. $P$ is on $AC$ and not on the extention of $AC$ from $A$ , st $\angle APS=\angle BAS$.Prove that $CS$ , the circle $(BPC)$ and the circle with diameter $AC$ are concurrent.