Locus
Source: Iran 2005
August 27, 2005
geometryrectanglegeometry proposed
Problem Statement
From each vertex of triangle we draw 3 arbitary parrallell lines, and from each vertex we draw a perpendicular to these lines. There are 3 rectangles that one of their diagnals is triangle's side. We draw their other diagnals and call them , and .
a) Prove that , and are concurrent at a point .
b) Find the locus of as we move the 3 arbitary lines.