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8
8
Part of
2014 Stanford Mathematics Tournament
Problems
(1)
SMT RMT 2014 Geometry #8
Source:
10/28/2022
O
O
O
is a circle with radius
1
1
1
.
A
A
A
and
B
B
B
are fixed points on the circle such that
A
B
=
2
AB =\sqrt2
A
B
=
2
. Let C be any point on the circle, and let
M
M
M
and
N
N
N
be the midpoints of
A
C
AC
A
C
and
B
C
BC
BC
, respectively. As
C
C
C
travels around circle
O
O
O
, find the area of the locus of points on
M
N
MN
MN
.
geometry