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2021 Stanford Mathematics Tournament
6
6
Part of
2021 Stanford Mathematics Tournament
Problems
(1)
SMT 2021 Geometry #6
Source:
8/9/2023
⊙
A
\odot A
⊙
A
, centered at point
A
A
A
, has radius
14
14
14
and
⊙
B
\odot B
⊙
B
, centered at point
B
B
B
, has radius
15
15
15
.
A
B
=
13
AB = 13
A
B
=
13
. The circles intersect at points
C
C
C
and
D
D
D
. Let
E
E
E
be a point on
⊙
A
\odot A
⊙
A
, and
F
F
F
be the point where line
E
C
EC
EC
intersects
⊙
B
\odot B
⊙
B
, again. Let the midpoints of
D
E
DE
D
E
and
D
F
DF
D
F
be
M
M
M
and
N
N
N
, respectively. Lines
A
M
AM
A
M
and
B
N
BN
BN
intersect at point
G
G
G
. If point
E
E
E
is allowed to move freely on
⊙
A
\odot A
⊙
A
, what is the radius of the locus of
G
G
G
?
geometry