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International Contests
Tournament Of Towns
1989 Tournament Of Towns
(228) 2
(228) 2
Part of
1989 Tournament Of Towns
Problems
(1)
TOT 228 1989 Autumn A J2 cyclic hexagon, AB=BC,CD=DE, EF=FA
Source:
3/12/2021
The hexagon
A
B
C
D
E
F
ABCDEF
A
BC
D
EF
is inscribed in a circle,
A
B
=
B
C
=
a
,
C
D
=
D
E
=
b
AB = BC = a, CD = DE = b
A
B
=
BC
=
a
,
C
D
=
D
E
=
b
, and
E
F
=
F
A
=
c
EF = FA = c
EF
=
F
A
=
c
. Prove that the area of triangle
B
D
F
BDF
B
D
F
equals half the area of the hexagon.(I.P. Nagel, Yevpatoria).
hexagon
Cyclic
geometry
areas