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6
2021 Geo #6: The duo of O and H
2021 Geo #6: The duo of O and H
Source:
May 30, 2021
geometry
circumcircle
Problem Statement
In triangle
A
B
C
ABC
A
BC
, let
M
M
M
be the midpoint of
B
C
BC
BC
,
H
H
H
be the orthocenter, and
O
O
O
be the circumcenter. Let
N
N
N
be the reflection of
M
M
M
over
H
H
H
. Suppose that
O
A
=
O
N
=
11
OA = ON = 11
O
A
=
ON
=
11
and
O
H
=
7.
OH = 7.
O
H
=
7.
Compute
B
C
2
BC^2
B
C
2
.
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