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Concyclic with China

Source: CSMO 2019 Grade 11 Problem 2

July 30, 2019
geometry

Problem Statement

ABCDABCD is a parallelogram with ∠BAD≠90\angle BAD \neq 90. Circle centered at AA radius BABA denoted as ω1\omega _1 intersects the extended side of AB,CBAB,CB at points E,FE,F respectively. Suppose the circle centered at DD with radius DADA, denoted as ω2\omega _2, intersects AD,CDAD,CD at points M,NM,N respectively. Suppose EN,FMEN,FM intersects at GG, AGAG intersects MEME at point TT. MFMF intersects ω1\omega _1 at Q≠FQ \neq F, and ENEN intersects ω2\omega _2 at P≠NP \neq N. Prove that G,P,T,QG,P,T,Q concyclic.
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