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2007 Harvard-MIT Mathematics Tournament
32
32
Part of
2007 Harvard-MIT Mathematics Tournament
Problems
(1)
2007 Guts #32: Circumcircles and Triangles
Source:
6/22/2012
Triangle
A
B
C
ABC
A
BC
has
A
B
=
4
AB=4
A
B
=
4
,
B
C
=
6
BC=6
BC
=
6
, and
A
C
=
5
AC=5
A
C
=
5
. Let
O
O
O
denote the circumcenter of
A
B
C
ABC
A
BC
. The circle
Γ
\Gamma
Γ
is tangent to and surrounds the circumcircles of triangle
A
O
B
AOB
A
OB
,
B
O
C
BOC
BOC
, and
A
O
C
AOC
A
OC
. Determine the diameter of
Γ
\Gamma
Γ
.
geometry
circumcircle