More problems

Problem 1. Given a straight line m and points A and B not lying on the same plane, determine on line m such a point C that the sum of the segments AC and CB be the least possible (Polish Mathematical Olympiad)

Problem 2. From all triangles inscribed in an acute triangle ABC find those with minimal perimeter.

Hint. If A₁ B₁ C₁ is one of them, where A₁ lies on BC, B₁ on AC and C₁ on AB reflect the point C₁ in lines AC and BC to obtain X and Y. If the point C₁ is fixed find A₁ and B₁, so that A₁ B₁ C₁ has minimal perimeter. After that leave C₁ to move along the side AB.