MathDB
Strange Collinearlity

Source: 2024 KJMO P3

November 9, 2024
geometryangle bisectorcircumcircle

Problem Statement

Acute triangle ABCABC satisfies ∠A>∠C\angle A > \angle C. Let D,E,FD, E, F be the points that the triangle's incircle intersects with BC,CA,ABBC, CA, AB, respectively, and PP some point on AFAF different from FF. The angle bisector of ∠ABC\angle ABC meets PQRPQR's circumcircle OO at L,RL, R. LL is the point closer to BB than RR. OO meets DF,DRDF, DR at point Q(≠F,L),S(≠R)Q(\neq F, L), S(\neq R) respectively, and PSPS hits segment BCBC at TT. Show that T,Q,LT, Q, L are collinear.
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