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Mathley Magazine
Geometry Mathley 2011-12
7.1
7.1
Part of
Geometry Mathley 2011-12
Problems
(1)
Geometry Mathley 7.1 EK = EL
Source:
6/7/2020
Let
A
B
C
D
ABCD
A
BC
D
be a cyclic quadrilateral. Suppose that
E
E
E
is the intersection of
A
B
AB
A
B
and
C
D
,
F
CD, F
C
D
,
F
is the intersection of
A
D
AD
A
D
and
C
B
,
I
CB, I
CB
,
I
is the intersection of
A
C
AC
A
C
and
B
D
BD
B
D
. The circumcircles
(
F
A
B
)
,
(
F
C
D
)
(FAB), (FCD)
(
F
A
B
)
,
(
FC
D
)
meet
F
I
FI
F
I
at
K
,
L
K, L
K
,
L
. Prove that
E
K
=
E
L
EK = EL
E
K
=
E
L
Nguyễn Minh Hà
geometry
circumcircle