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Intermediate Geometry in 2024 IMOC

Source: 2024 imocsl G5 (Night 3-G)

August 8, 2024
geometryIMOC

Problem Statement

Triangle ABCABC satisfying AB<ACAB<AC has circumcircle Ω\Omega. E,FE, F lies on AC,ABAC, AB, respectively, such that BCEFBCEF is cyclic. TT lies on EFEF such that ⊙(TEF)\odot(TEF) is tangent to BCBC at TT. A′A' is the antipode of AA on Ω\Omega. TA′,TATA', TA intersects Ω\Omega again at X,YX, Y, respectively, and EFEF intersects ⊙(TXY)\odot(TXY) again at WW. Prove that ∡WBA=∡ACW\measuredangle WBA=\measuredangle ACW
Proposed by BlessingOfHeaven
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