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AO/AD + BO/BE + CO / CF=2 wanted, cevians related

Source: 2004 Indonedia MO Province P2 q2 OSP

December 11, 2020
geometryratioCevians

Problem Statement

Triangle ABCABC is given. The points D,ED, E, and FF are located on the sides BC,CABC, CA and ABAB respectively so that the lines AD,BEAD, BE and CFCF intersect at point OO. Prove that AOAD+BOBE+COCF=2\frac{AO}{AD} + \frac{BO}{BE} + \frac{CO}{ CF}=2
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