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Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad Regional Round
1993 All-Russian Olympiad Regional Round
9.3
9.3
Part of
1993 All-Russian Olympiad Regional Round
Problems
(1)
ABC necessarily isosceles ? All-Russian MO 1993 Regional (R4) 9.3
Source:
8/26/2024
Points
M
M
M
and
N
N
N
are chosen on the sides
A
B
AB
A
B
and BC of a triangle
A
B
C
ABC
A
BC
. The segments
A
N
AN
A
N
and
C
M
CM
CM
meet at
O
O
O
such that
A
O
=
C
O
AO =CO
A
O
=
CO
. Is the triangle
A
B
C
ABC
A
BC
necessarily isosceles, if(a)
A
M
=
C
N
AM = CN
A
M
=
CN
?(b)
B
M
=
B
N
BM = BN
BM
=
BN
?
geometry
isosceles