MathDB
iff Iran Lemma

Source: Indonesia TST Round 1-geometry

March 3, 2024
TststgeometryincenterIndonesiaIndonesia TST

Problem Statement

Given an acute triangle ABCABC. The incircle with center II touches BC,CA,ABBC,CA,AB at D,E,FD,E,F respectively. Let M,NM,N be the midpoint of the minor arc of ABAB and ACAC respectively. Prove that M,F,E,NM,F,E,N are collinear if and only if ∠BAC=90\angle BAC =90∘^{\circ}
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