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National and Regional Contests
USA Contests
MAA AMC
USAMO
1994 USAMO
3
hexagon
hexagon
Source: USAMO 1994/3
August 9, 2005
Problem Statement
A convex hexagon
A
B
C
D
E
F
ABCDEF
A
BC
D
EF
is inscribed in a circle such that
A
B
=
C
D
=
E
F
AB = CD = EF
A
B
=
C
D
=
EF
and diagonals
A
D
AD
A
D
,
B
E
BE
BE
, and
C
F
CF
CF
are concurrent. Let
P
P
P
be the intersection of
A
D
AD
A
D
and
C
E
CE
CE
. Prove that
C
P
/
P
E
=
(
A
C
/
C
E
)
2
CP/PE = (AC/CE)^2
CP
/
PE
=
(
A
C
/
CE
)
2
.
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