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SNOW in Taiwan

Source: 2022 Taiwan TST Round 3 Mock Day 2 P5

April 30, 2022
circumcircleConcyclicgeometry

Problem Statement

Let ABCABC be an acute triangle with circumcenter OO and circumcircle Ω\Omega. Choose points D,ED, E from sides AB,ACAB, AC, respectively, and let ℓ\ell be the line passing through AA and perpendicular to DEDE. Let ℓ\ell intersect the circumcircle of triangle ADEADE and Ω\Omega again at points P,QP, Q, respectively. Let NN be the intersection of OQOQ and BCBC, SS be the intersection of OPOP and DEDE, and WW be the orthocenter of triangle SAOSAO.
Prove that the points SS, NN, OO, WW are concyclic.
Proposed by Li4 and me.
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