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Tangent circles to random line yielding cyclic quadrilateral

Source: Netherlands IMO TST #3 2019 P1

July 16, 2019
geometrycyclic quadrilateral

Problem Statement

Let ABCDABCD be a cyclic quadrilateral (In the same order) inscribed into the circle ⊙(O)\odot (O). Let AC‾\overline{AC} ∩\cap BD‾\overline{BD} == EE. A randome line ℓ\ell through EE intersects AB‾\overline{AB} at PP and BCBC at QQ. A circle ω\omega touches ℓ\ell at EE and passes through DD. Given, ω\omega ∩\cap ⊙(O)\odot (O) == RR. Prove, Points B,Q,R,PB,Q,R,P are concyclic.
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