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Bangladesh Contests
Bangladesh Mathematical Olympiad
2018 Bangladesh Mathematical Olympiad
5
5
Part of
2018 Bangladesh Mathematical Olympiad
Problems
(1)
Four circles and quadrilateral
Source: BdMO 18
2/27/2019
Four circles are drawn with the sides of quadrilateral
A
B
C
D
ABCD
A
BC
D
as diameters. The two circles passing through
A
A
A
meet again at
E
E
E
. The two circles passing through
B
B
B
meet again at
F
F
F
. The two circles passing through
C
C
C
meet again at
G
G
G
. The two circles passing through
D
D
D
meet again at
H
H
H
. Suppose,
E
,
F
,
G
,
H
E, F, G,H
E
,
F
,
G
,
H
are all distinct. Is the quadrilateral
E
F
G
H
EFGH
EFG
H
similar to
A
B
C
D
ABCD
A
BC
D
? Show with proof.
geometry