MathDB

In a scalene triangle

ABC

D

is the foot of the altitude through

A

E

is the intersection of

AC

with the bisector of

\angle ABC

and

F

is a point on

AB

. Let

O

the circumcenter of

ABC

and

X=AD\cap BE

Y=BE\cap CF

Z=CF \cap AD

. If

XYZ

is an equilateral triangle, prove that one of the triangles

OXY

OYZ

OZX

must be equilateral.

Problem Statement