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Prove two lines are parallel

Source: Mathematics Regional Olympiad of Mexico Southeast 2019 P4

October 23, 2021
geometryparallel

Problem Statement

Let Γ\Gamma a circumference. TT a point in Γ\Gamma, PP and AA two points outside Γ\Gamma such that PTPT is tangent to Γ\Gamma and PA=PTPA=PT. Let CC a point in Γ(C≠T)\Gamma (C\neq T), ACAC and PCPC intersect again Γ\Gamma in DD and BB, respectively. ABAB intersect Γ\Gamma in EE. Prove that DEDE it´s parallel to APAP
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