MathDB

Let

ABC

be a triangle. A point

D

lies on line

BC

and points

E,F

are taken on

AC,AB

such that

DE \parallel AB

and

DF\parallel AC

. Let

G = (AEF) \cap (ABC) \neq A

and

I = (DEF) \cap BC\neq D

. Let

H

and

O

denote the orthocenter and the circumcenter of triangle

DEF

. Prove that

A,O,I

are collinear if and only if

G,H,I

are collinear.
Proposed by Kaan Bilge

Problem Statement