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National and Regional Contests
Russia Contests
All-Russian Olympiad
1981 All Soviet Union Mathematical Olympiad
315
315
Part of
1981 All Soviet Union Mathematical Olympiad
Problems
(1)
ASU 315 All Soviet Union MO 1981 4 parallelograms => 5th one
Source:
7/23/2019
The quadrangles
A
M
B
E
,
A
H
B
T
,
B
K
X
M
AMBE, AHBT, BKXM
A
MBE
,
A
H
BT
,
B
K
XM
, and
C
K
X
P
CKXP
C
K
XP
are parallelograms. Prove that the quadrangle
A
B
T
E
ABTE
A
BTE
is also parallelogram. (the vertices are mentioned counterclockwise)
geometry
parallelogram