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China Contests
China Northern MO
2013 China Northern MO
3
3
Part of
2013 China Northern MO
Problems
(1)
fixed length wanted, circle passing through 2 fixed points
Source: China Northern MO 2013 p3 CNMO
10/28/2022
As shown in figure ,
A
,
B
A,B
A
,
B
are two fixed points of circle
ā
O
\odot O
ā
O
,
C
C
C
is the midpoint of the major arc
A
B
AB
A
B
,
D
D
D
is any point of the minor arc
A
B
AB
A
B
. Tangent at
D
D
D
intersects tangents at
A
,
B
A,B
A
,
B
at points
E
,
F
E,F
E
,
F
respectively. Segments
C
E
CE
CE
and
C
F
CF
CF
intersect chord
A
B
AB
A
B
at points
G
G
G
and
H
H
H
respectively. Prove that the length of line segment
G
H
GH
G
H
has a fixed value. https://cdn.artofproblemsolving.com/attachments/9/2/85227f169193f61e313293e9128f6ece2ff1f7.png
geometry
fixed