MathDB
concurrent wanted, midpoints, incenters related

Source: 2016 Thailand October Camp 1.1

October 15, 2020
geometryincenterconcurrencyconcurrentmidpoints

Problem Statement

In △ABC,D,E,F\vartriangle ABC, D, E, F are the midpoints of AB,BC,CAAB, BC, CA respectively. Denote by OA,OB,OCO_A, O_B, O_C the incenters of △ADF,△BED,△CFE\vartriangle ADF, \vartriangle BED, \vartriangle CFE respectively. Prove that OAE,OBF,OCDO_AE, O_BF, O_CD are concurrent.
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