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Point P in triangle BHC

Source: Iran TST 2023 ; Exam 1 Problem 6

March 16, 2023
geometrycircumcircle

Problem Statement

ABCABC is an acute triangle with orthocenter HH. Point PP is in triangle BHCBHC that ∠HPC=3∠HBC\angle HPC = 3 \angle HBC and ∠HPB=3∠HCB\angle HPB =3 \angle HCB . Reflection of point PP through BH,CHBH,CH is X,YX,Y. if SS is the center of circumcircle of AXYAXY , Prove that: ∠BAS=∠CAP\angle BAS = \angle CAP
Proposed by Pouria Mahmoudkhan Shirazi
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