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inequality with cevians in equilateral

Source: Nordic Mathematical Contest 1994 #1

October 4, 2017
inequalitiesEquilateral Triangle

Problem Statement

Let OO be an interior point in the equilateral triangle ABCABC, of side length aa. The lines AO,BOAO, BO, and COCO intersect the sides of the triangle in the points A1,B1A_1, B_1, and C1C_1. Show that OA1+OB1+OC1<aOA_1 + OB_1 + OC_1 < a.
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