<Tri-2025-2213>, hint

A'(0,0), B(-a,0), C(a,0) A(d,h), D(d,0) AD is altitude, M(d, h/2)

tan<PCB=sinC cosB -->2R tan <PCB=2R sinC cosB. Let R be radius of the circumcircle 

of ABC. Q(-a, h). AA': y=h/d x BM: y=h/2(d+a){(x+a)}

Calculation shows line CP pass through  Q(-a, h)