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2021 Indonesia MO
2
2
Part of
2021 Indonesia MO
Problems
(1)
An easy geometry about midpoints
Source: Indonesia National Math Olympiad 2021 Problem 2 (INAMO 2021/2)
11/8/2021
Let
A
B
C
ABC
A
BC
be an acute triangle. Let
D
D
D
and
E
E
E
be the midpoint of segment
A
B
AB
A
B
and
A
C
AC
A
C
respectively. Suppose
L
1
L_1
L
1
and
L
2
L_2
L
2
are circumcircle of triangle
A
B
C
ABC
A
BC
and
A
D
E
ADE
A
D
E
respectively.
C
D
CD
C
D
intersects
L
1
L_1
L
1
and
L
2
L_2
L
2
at
M
(
M
≠
C
)
M (M \not= C)
M
(
M
=
C
)
and
N
(
N
≠
D
)
N (N \not= D)
N
(
N
=
D
)
. If
D
M
=
D
N
DM = DN
D
M
=
D
N
, prove that
△
A
B
C
\triangle ABC
△
A
BC
is isosceles.
geometry
circumcircle