MathDB
Triangle

Source: RMO 2003, Grade 7, Problem 4

October 23, 2008
geometryparallelogram

Problem Statement

In triangle ABC ABC, P P is the midpoint of side BC BC. Let M∈(AB) M\in(AB), N∈(AC) N\in(AC) be such that MN∥BC MN\parallel BC and {Q} \{Q\} be the common point of MP MP and BN BN. The perpendicular from Q Q on AC AC intersects AC AC in R R and the parallel from B B to AC AC in T T. Prove that: (a) TP∥MR TP\parallel MR; (b) \angle MRQ\equal{}\angle PRQ. Mircea Fianu
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