IMO 1987 LL NET47

Through a point P within a triangle ABC the lines l, m, and

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IMO 1987 LL NET47

Origin: NET

Problem

Through a point P within a triangle ABC the lines l, m, and n perpendicular respectively to AP, BP, CP are drawn. Prove that if l intersects the line BC in Q, m intersects AC in R, and n intersects AB in S, then the points Q, R, and S are collinear.