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Sharygin Geometry Olympiad
2019 Sharygin Geometry Olympiad
13
13
Part of
2019 Sharygin Geometry Olympiad
Problems
(1)
Sharygin CR 2019 P13
Source: Sharygin CR 2019 P13 (Grade 9 - 10)
3/6/2019
Let
A
B
C
ABC
A
BC
be an acute-angled triangle with altitude
A
T
=
h
AT = h
A
T
=
h
. The line passing through its circumcenter
O
O
O
and incenter
I
I
I
meets the sides
A
B
AB
A
B
and
A
C
AC
A
C
at points
F
F
F
and
N
N
N
, respectively. It is known that
B
F
N
C
BFNC
BFNC
is a cyclic quadrilateral. Find the sum of the distances from the orthocenter of
A
B
C
ABC
A
BC
to its vertices.
geometry