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chord of a circle tangent to another circle

Source: Irmo 2018 p1 q5

September 16, 2018
geometrytangentcircles

Problem Statement

Points A,BA, B and PP lie on the circumference of a circle Ω1\Omega_1 such that ∠APB\angle APB is an obtuse angle. Let QQ be the foot of the perpendicular from PP on ABAB. A second circle Ω2\Omega_2 is drawn with centre PP and radius PQPQ. The tangents from AA and BB to Ω2\Omega_2 intersect Ω1\Omega_1 at FF and HH respectively. Prove that FHFH is tangent to Ω2\Omega_2.
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