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Problems
Contests
National and Regional Contests
China Contests
South East Mathematical Olympiad
2020 South East Mathematical Olympiad
6
6
Part of
2020 South East Mathematical Olympiad
Problems
(1)
Pedal circle related
Source: 2020 China Southeast 10.6/11.6
8/7/2020
In a quadrilateral
A
B
C
D
ABCD
A
BC
D
,
∠
A
B
C
=
∠
A
D
C
<
9
0
∘
\angle ABC=\angle ADC <90^{\circ}
∠
A
BC
=
∠
A
D
C
<
9
0
∘
. The circle with diameter
A
C
AC
A
C
intersects
B
C
BC
BC
and
C
D
CD
C
D
again at
E
,
F
E,F
E
,
F
, respectively.
M
M
M
is the midpoint of
B
D
BD
B
D
, and
A
N
⊥
B
D
AN \perp BD
A
N
⊥
B
D
at
N
N
N
. Prove that
M
,
N
,
E
,
F
M,N,E,F
M
,
N
,
E
,
F
is concyclic.
geometry
Isogonal conjugate