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Contests
National and Regional Contests
Ecuador Contests
Ecuador Juniors
2019 Ecuador Juniors
4
4
Part of
2019 Ecuador Juniors
Problems
(1)
square inside a square, AE = BF = CG = DH - 2019 Ecuador Juniors (OMEC) L2 p4
Source:
10/24/2022
Let
A
B
C
D
ABCD
A
BC
D
be a square. On the segments
A
B
AB
A
B
,
B
C
BC
BC
,
C
D
CD
C
D
and
D
A
DA
D
A
, choose points
E
,
F
,
G
E, F, G
E
,
F
,
G
and
H
H
H
, respectively, such that
A
E
=
B
F
=
C
G
=
D
H
AE = BF = CG = DH
A
E
=
BF
=
CG
=
DH
. Let
P
P
P
be the intersection point of
A
F
AF
A
F
and
D
E
DE
D
E
,
Q
Q
Q
be the intersection point of
B
G
BG
BG
and
A
F
AF
A
F
,
R
R
R
the intersection point of
C
H
CH
C
H
and
B
G
BG
BG
, and
S
S
S
the point of intersection of
D
E
DE
D
E
and
C
H
CH
C
H
. Prove that
P
Q
R
S
PQRS
PQRS
is a square.
geometry
square