Parallel lines through inner point of triangle - Austria '10
Source:
May 13, 2010
geometryparallelogramincenterperimetergeometry proposed
Problem Statement
The the parallel lines through an inner point of triangle split the triangle into three parallelograms and three triangles adjacent to the sides of .
(a) Show that if is the incenter, the perimeter of each of the three small triangles equals the length of the adjacent side.
(b) For a given triangle , determine all inner points such that the perimeter of each of the three small triangles equals the length of the adjacent side.
(c) For which inner point does the sum of the areas of the three small triangles attain a minimum?(41st Austrian Mathematical Olympiad, National Competition, part 1, Problem 4)