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Variable points for triangle

Source: St Petersburg Olympiad 2018, Grade 9, P3

June 22, 2018
geometry

Problem Statement

ABCABC is acuteangled triangle. Variable point XX lies on segment ACAC, and variable point YY lies on the ray BCBC but not segment BCBC, such that ∠ABX+∠CXY=90\angle ABX+\angle CXY =90. TT is projection of BB on the XYXY. Prove that all points TT lies on the line.
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