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China Northern MO
2023 China Northern MO
1
1
Part of
2023 China Northern MO
Problems
(1)
concyclic wanted, diameter related
Source: China Northern MO 2023 p1 CNMO
5/5/2024
As shown in the figure,
A
B
AB
A
B
is the diameter of circle
⊙
O
\odot O
⊙
O
, and chords
A
C
AC
A
C
and
B
D
BD
B
D
intersect at point
E
E
E
,
E
F
⊥
A
B
EF\perp AB
EF
⊥
A
B
intersects at point
F
F
F
, and
F
C
FC
FC
intersects
B
D
BD
B
D
at point
G
G
G
. Point
M
M
M
lies on
A
B
AB
A
B
such that
M
D
=
M
G
MD=MG
M
D
=
MG
. Prove that points
F
F
F
,
M
M
M
,
D
D
D
,
G
G
G
lies on a circle. https://cdn.artofproblemsolving.com/attachments/2/3/614ef5b9e8c8b16a29b8b960290ef9d7297529.jpg
geometry
Concyclic