MathDB

Let

ABC

be an acute-angled triangle with altitude

AT = h

. The line passing through its circumcenter

O

and incenter

I

meets the sides

AB

and

AC

at points

F

and

N

, respectively. It is known that

BFNC

is a cyclic quadrilateral. Find the sum of the distances from the orthocenter of

ABC

to its vertices.

Problem Statement