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Another triangle geo

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

August 16, 2023
geometry

Problem Statement

In the acute triangle △ABC\triangle ABC , HH is the orthocenter. SS is a point on (AHC)(AHC) st ∠ASB=90\angle ASB = 90. PP is on ACAC and not on the extention of ACAC from AA , st ∠APS=∠BAS\angle APS=\angle BAS.Prove that CSCS , the circle (BPC)(BPC) and the circle with diameter ACAC are concurrent.
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