MathDB

4 orthocenters form a rectangle

Source: Balkan MO 2002, problem 3

April 24, 2006

geometryrectanglegeometric transformationhomothetyreflectioncircumcircleparallelogram

Problem Statement

Two circles with different radii intersect in two points

A

and

B

. Let the common tangents of the two circles be

MN

and

ST

such that

M,S

lie on the first circle, and

N,T

on the second. Prove that the orthocenters of the triangles

AMN

AST

BMN

and

BST

are the four vertices of a rectangle.