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Prove a point does not depend of the choice of other point

Source: Mathematics Regional Olympiad of Mexico Southeast 2021 P1

October 22, 2021
geometryTangents

Problem Statement

Let A,BA, B and CC three points on a line ll, in that order .Let DD a point outside ll and Γ\Gamma the circumcircle of △BCD\triangle BCD, the tangents from AA to Γ\Gamma touch Γ\Gamma on SS and TT. Let PP the intersection of STST and ACAC. Prove that PP does not depend of the choice of DD.
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