MathDB
Problems
Contests
National and Regional Contests
Russia Contests
All-Russian Olympiad
1981 All Soviet Union Mathematical Olympiad
312
312
Part of
1981 All Soviet Union Mathematical Olympiad
Problems
(1)
ASU 312 All Soviet Union MO 1981 (KLMN) =1/2 (ABCD), areas
Source:
7/23/2019
The points
K
K
K
and
M
M
M
are the centres of the
A
B
AB
A
B
and
C
D
CD
C
D
sides of the convex quadrangle
A
B
C
D
ABCD
A
BC
D
. The points
L
L
L
and
M
M
M
belong to two other sides and
K
L
M
N
KLMN
K
L
MN
is a rectangle. Prove that
K
L
M
N
KLMN
K
L
MN
area is a half of
A
B
C
D
ABCD
A
BC
D
area.
geometry
rectangle