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Part of 2004 Bosnia and Herzegovina Team Selection Test

Problems(1)

Bosnia and Herzegovina TST 2004 Day 2 Problem 3

Source: Bosnia and Herzegovina Team Selection Test 2004

9/17/2018
It is given triangle ABCABC and parallelogram ASCRASCR with diagonal ACAC. Let line constructed through point BB parallel with CSCS intersects line ASAS and CRCR in MM and PP, respectively. Let line constructed through point BB parallel with ASAS intersects line ARAR and CSCS in NN and QQ, respectively. Prove that lines RSRS, MNMN and PQPQ are concurrent
geometryparallelogramconcurrent