Ratio between areas in a triangle divided by 3 lines
Source: Nordic MO 2009 Q1
April 20, 2013
ratiogeometrygeometry unsolved
Problem Statement
A point is chosen in an arbitrary triangle. Three lines are drawn through which are parallel to the sides of the triangle. The lines divide the triangle into three smaller triangles and three parallelograms. Let be the ratio between the total area of the three smaller triangles and the area of the given triangle. Prove that and determine those points for which .