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Problems
Contests
National and Regional Contests
Brazil Contests
Brazil National Olympiad
1984 Brazil National Olympiad
5
5
Part of
1984 Brazil National Olympiad
Problems
(1)
4 squares outside a convex quadrilateral, centers's distances equal & _|_
Source: Brazilian Mathematical Olympiad 1984 P5
7/27/2018
A
B
C
D
ABCD
A
BC
D
is any convex quadrilateral. Squares center
E
,
F
,
G
,
H
E, F, G, H
E
,
F
,
G
,
H
are constructed on the outside of the edges
A
B
,
B
C
,
C
D
AB, BC, CD
A
B
,
BC
,
C
D
and
D
A
DA
D
A
respectively. Show that
E
G
EG
EG
and
F
H
FH
F
H
are equal and perpendicular.
geometry
Squares
convex quadrilateral