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Official Ukraine Selection Cycle
Kyiv City MO
Kyiv City MO - geometry
Kyiv City MO Juniors 2003+ geometry
2020.8.51
2020.8.51
Part of
Kyiv City MO Juniors 2003+ geometry
Problems
(1)
concurrency in cyclic hexagon,AB=BC, CD=DE, EF=FA (2020 Kyiv City MO 8.5.1)
Source:
9/20/2020
Let
A
B
C
D
E
F
ABCDEF
A
BC
D
EF
be a hexagon inscribed in a circle in which
A
B
=
B
C
,
C
D
=
D
E
AB = BC, CD = DE
A
B
=
BC
,
C
D
=
D
E
and
E
F
=
F
A
EF = FA
EF
=
F
A
. Prove that the lines
A
D
,
B
E
AD, BE
A
D
,
BE
and
C
F
CF
CF
intersect at one point.
geometry
concurrency
concurrent
Cyclic
hexagon
equal segments