MathDB
Sufficient condition for a point to lie on a median

Source: Romanian National Olympiad, grade ix, p.3

August 23, 2019
geometrymedianarea

Problem Statement

Let be a point P P in the interior of a triangle ABC. ABC. The lines AP,BP,CP AP,BP,CP meet BC,AC, BC,AC, respectively, AB AB at A1,B1, A_1,B_1, respectively, C1. C_1. If APBA1+APCB1+APAC1=12AABC, \mathcal{A}_{PBA_1} +\mathcal{A}_{PCB_1} +\mathcal{A}_{PAC_1} =\frac{1}{2}\mathcal{A}_{ABC} , show that P P lies on a median of ABC. ABC.
A \mathcal{A} denotes area.
Back to ProblemsView on AoPS