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International Contests
APMO
1993 APMO
1
1
Part of
1993 APMO
Problems
(1)
60 degree angle
Source: APMO 1993
3/11/2006
Let
A
B
C
D
ABCD
A
BC
D
be a quadrilateral such that all sides have equal length and
∠
A
B
C
=
6
0
o
\angle{ABC} =60^o
∠
A
BC
=
6
0
o
. Let
l
l
l
be a line passing through
D
D
D
and not intersecting the quadrilateral (except at
D
D
D
). Let
E
E
E
and
F
F
F
be the points of intersection of
l
l
l
with
A
B
AB
A
B
and
B
C
BC
BC
respectively. Let
M
M
M
be the point of intersection of
C
E
CE
CE
and
A
F
AF
A
F
. Prove that
C
A
2
=
C
M
×
C
E
CA^2 = CM \times CE
C
A
2
=
CM
×
CE
.
geometry
circumcircle