MathDB

concurrency wanted, centers of 3 rectangles related, wrt a triangle

Source: 2003 Oral Moscow Geometry Olympiad grade 9 p5

October 26, 2020

geometryrectangleconcurrencyconcurrent

Problem Statement

Given triangle

ABC

. Point

O_1

is the center of the

BCDE

rectangle, constructed so that the side

DE

of the rectangle contains the vertex

A

of the triangle. Points

O_2

and

O_3

are the centers of rectangles constructed in the same way on the sides

AC

and

AB

, respectively. Prove that lines

AO_1, BO_2

and

CO_3

meet at one point.