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Centroid Inside Triangle

Source: Iran TST 3, Day 1, Problem 1

May 12, 2013
geometrygeometric transformationreflectionparallelogramperimeterhomothetyratio

Problem Statement

PP is an arbitrary point inside acute triangle ABCABC. Let A1,B1,C1A_1,B_1,C_1 be the reflections of point PP with respect to sides BC,CA,ABBC,CA,AB. Prove that the centroid of triangle A1B1C1A_1B_1C_1 lies inside triangle ABCABC.
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