MathDB
Incircle geo with equal segments

Source: IMSC 2023 Mock IMO P4

July 13, 2023
geometry

Problem Statement

Let ABCABC be a triangle with incenter II and let AIAI meet BCBC at DD. Let EE be a point on the segment ACAC, such that CD=CECD=CE and let FF be on the segment ABAB such that BF=BDBF=BD. Let (CEI)∩(DFI)=P≠I(CEI) \cap (DFI)=P \neq I and (BFI)∩(DEI)=Q≠I(BFI) \cap (DEI)=Q \neq I. Prove that PQ⊥BCPQ \perp BC.
Proposed by Leonardo Franchi, Italy
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