MathDB
Problems
Contests
National and Regional Contests
Russia Contests
Saint Petersburg Mathematical Olympiad
2013 Saint Petersburg Mathematical Olympiad
2
St.Peterburg, P2 Grade 10, 2013
St.Peterburg, P2 Grade 10, 2013
Source:
April 27, 2014
geometry proposed
geometry
Problem Statement
in a convex quadrilateral
A
B
C
D
ABCD
A
BC
D
,
M
,
N
M,N
M
,
N
are midpoints of
B
C
,
A
D
BC,AD
BC
,
A
D
respectively. If
A
M
=
B
N
AM=BN
A
M
=
BN
and
D
M
=
C
N
DM=CN
D
M
=
CN
then prove that
A
C
=
B
D
AC=BD
A
C
=
B
D
.S. Berlov
Back to Problems
View on AoPS