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Part of 2013 JBMO TST - Macedonia

Problems(1)

Areas

Source: Macedonian JBMO TST 2013

5/26/2013
A triangle ABC ABC is given, and a segment PQ=t PQ=t on BC BC such that P P is between B B and Q Q and Q Q is between P P and C C . Let PP1∣∣AB PP_1 || AB , P1 P_1 is on AC AC , and PP2∣∣AC PP_2 || AC , P2 P_2 is on AB AB . Points Q1 Q_1 and Q2 Q_2 аrе defined similar. Prove that the sum of the areas of PQQ1P1 PQQ_1P_1 and PQQ2P2 PQQ_2P_2 does not depend from the position of PQ PQ on BC BC .
geometrygeometry proposed