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National and Regional Contests
Korea Contests
Korea Junior Mathematics Olympiad
2012 Korea Junior Math Olympiad
2
2
Part of
2012 Korea Junior Math Olympiad
Problems
(1)
concyclic, starting with an inscribed pentagon
Source: KJMO 2012 p2
5/3/2019
A pentagon
A
B
C
D
E
ABCDE
A
BC
D
E
is inscribed in a circle
O
O
O
, and satis fies
∠
A
=
9
0
o
,
A
B
=
C
D
\angle A = 90^o, AB = CD
∠
A
=
9
0
o
,
A
B
=
C
D
. Let
F
F
F
be a point on segment
A
E
AE
A
E
. Let
B
F
BF
BF
hit
O
O
O
again at
J
(
≠
B
)
J(\ne B)
J
(
=
B
)
,
C
E
∩
D
J
=
K
CE \cap DJ = K
CE
∩
D
J
=
K
,
B
D
∩
F
K
=
L
BD\cap FK = L
B
D
∩
F
K
=
L
. Prove that
B
,
L
,
E
,
F
B,L,E,F
B
,
L
,
E
,
F
are cyclic.
geometry
pentagon
Concyclic