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Rioplatense Mathematical Olympiad, Level 3
2019 Rioplatense Mathematical Olympiad, Level 3
1
1
Part of
2019 Rioplatense Mathematical Olympiad, Level 3
Problems
(1)
Hexagon and square
Source: Rioplatense Olympiad L3 2019
12/10/2019
Let
A
B
C
D
E
F
ABCDEF
A
BC
D
EF
be a regular hexagon, in the sides
A
B
AB
A
B
,
C
D
CD
C
D
,
D
E
DE
D
E
and
F
A
FA
F
A
we choose four points
P
,
Q
,
R
P,Q,R
P
,
Q
,
R
and
S
S
S
respectively, such that
P
Q
R
S
PQRS
PQRS
is a square. Prove that
P
Q
PQ
PQ
and
B
C
BC
BC
are parallel.
geometry