MathDB

Prove that a line passes through the orthocenter

Source: Iberoamerican Olympiad 2005

September 29, 2005

geometrycircumcircletrigonometrygeometry solved

Problem Statement

Let

O

be the circumcenter of acutangle triangle

ABC

and let

A_1

be some point in the smallest arc

AC

of the circumcircle of

ABC

. Let

A_2

and

A_3

points on sides

AB

and

AC

, respectively, such that

\angle BA_1A_2 = \angle OAC

and

\angle CA_1A_3 = \angle OAB

. Prove that the line

A_2A_3

passes through the orthocenter of

ABC

.

Back to Problems View on AoPS