MathDB
Problems
Contests
International Contests
CentroAmerican
2019 Centroamerican and Caribbean Math Olympiad
3
3
Part of
2019 Centroamerican and Caribbean Math Olympiad
Problems
(1)
2019 Central American and Caribbean Mathematical Olympiad, P3
Source:
6/18/2019
Let
A
B
C
ABC
A
BC
be a triangle and
Γ
\Gamma
Γ
its circumcircle. Let
D
D
D
be the foot of the altitude from
A
A
A
to the side
B
C
BC
BC
,
M
M
M
and
N
N
N
the midpoints of
A
B
AB
A
B
and
A
C
AC
A
C
, and
Q
Q
Q
the point on
Γ
\Gamma
Γ
diametrically opposite to
A
A
A
. Let
E
E
E
be the midpoint of
D
Q
DQ
D
Q
. Show that the lines perpendicular to
E
M
EM
EM
and
E
N
EN
EN
passing through
M
M
M
and
N
N
N
, respectively, meet on
A
D
AD
A
D
.
geometry
circumcircle