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Kvant 2019
M2583
M2583
Part of
Kvant 2019
Problems
(1)
Nice collinearity in regular pentagon
Source: Kvant Magazine No.11 2019 M2583
3/14/2023
On the side
D
E
DE
D
E
and on the diagonal
B
E
BE
BE
of the regular pentagon
A
B
C
D
E
ABCDE
A
BC
D
E
we consider the squares
D
E
F
G
DEFG
D
EFG
and
B
E
H
I
BEHI
BE
H
I
.[*] Prove that
A
,
I
,
A,I,
A
,
I
,
and
G
G
G
are collinear. [*] Prove that on this line lies also the centre
O
O
O
of the square
B
D
J
K
BDJK
B
D
J
K
.
geometry
pantagon
Kvant