MathDB
Romanian District Olympiad 2015, Grade VII, Problem 3

Source:

September 25, 2018
geometry

Problem Statement

On the segment AC AC of the triangle ABC, ABC, let M M be the midpoint of it, and let N N a point on AM, AM, distinct from A A and M. M. The parallel through N N with respect to AB AB intersects BM BM on P, P, the parallel through M M with respect to BC BC intersects BN BN on Q, Q, and the parallel through N N with respect to AQ AQ intersects BC BC on S. S. Prove that PS PS and AC AC are parallel.
Back to ProblemsView on AoPS