MathDB

right triangle and squares externally drawn

Source: 16-th Hungary-Israel Binational Mathematical Competition 2005

March 29, 2007

geometryperimetergeometric transformationhomothetygeometry unsolved

Problem Statement

Squares

ABB_{1}A_{2}

and

BCC_{1}B_{2}

are externally drawn on the hypotenuse

AB

and on the leg

BC

of a right triangle

ABC

. Show that the lines

CA_{2}

and

AB_{2}

meet on the perimeter of a square with the vertices on the perimeter of triangle

ABC .