MathDB

Let

ABC

be an acute-angled triangle with

AB \ne AC

, and let

I

and

O

be its incenter and circumcenter, respectively. Let the incircle touch

BC, CA

and

AB

D, E

and

F

, respectively. Assume that the line through

I

parallel to

EF

, the line through

D

parallel to

AO

, and the altitude from

A

are concurrent. Prove that the concurrency point is the orthocenter of the triangle

ABC

.
Petar Nizic-Nikolac, Croatia

Problem Statement