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2023-IMOC
G1
G1
Part of
2023-IMOC
Problems
(1)
Configuration with a paralellogram
Source: IMOC 2023 G1
9/9/2023
Triangle
A
B
C
ABC
A
BC
has circumcenter
O
O
O
.
M
M
M
is the midpoint of arc
B
C
BC
BC
not containing
A
A
A
.
S
S
S
is a point on
(
A
B
C
)
(ABC)
(
A
BC
)
such that
A
S
AS
A
S
and
B
C
BC
BC
intersect on the line passing through
O
O
O
and perpendicular to
A
M
AM
A
M
.
D
D
D
is a point such that
A
B
D
C
ABDC
A
B
D
C
is a parallelogram. Prove that
D
D
D
lies on the line
S
M
SM
SM
.
geometry
parallelogram