MathDB

In an acute triangle

ABC

with

|AB| \not= |AC|

, let

I

be the incenter and

O

the circumcenter. The incircle is tangent to

\overline{BC}, \overline{CA}

and

\overline{AB}

D,E

and

F

respectively. Prove that if the line parallel to

EF

passing through

I

, the line parallel to

AO

passing through

D

and the altitude from

A

are concurrent, then the point of concurrence is the orthocenter of the triangle

ABC

.
Proposed by Petar Nizié-Nikolac

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