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National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
2000 All-Russian Olympiad Regional Round
9.7
9.7
Part of
2000 All-Russian Olympiad Regional Round
Problems
(1)
OD _|_ AB - All-Russian MO 2000 Regional (R4) 9.7
Source:
9/26/2024
On side
A
B
AB
A
B
of triangle
A
B
C
ABC
A
BC
, point
D
D
D
is selected. Circle circumscribed around triangle
B
C
D
BCD
BC
D
, intersects side
A
C
AC
A
C
at point
M
M
M
, and the circumcircle of triangle
A
C
D
ACD
A
C
D
intersects the side
B
C
BC
BC
at point
N
N
N
(
M
,
N
≠
C
M,N \ne C
M
,
N
=
C
). Let
O
O
O
be the circumcenter of the triangle
C
M
N
CMN
CMN
. Prove that line
O
D
OD
O
D
is perpendicular to side
A
B
AB
A
B
.
geometry
perpendicular