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B5
B5
Part of
2011 Princeton University Math Competition
Problems
(1)
2011 PUMaC Geometry B5
Source:
9/24/2019
Four circles are situated in the plane so that each is tangent to the other three. If three of the radii are
5
5
5
,
5
5
5
, and
8
8
8
, the largest possible radius of the fourth circle is
a
/
b
a/b
a
/
b
, where
a
a
a
and
b
b
b
are positive integers and gcd
(
a
,
b
)
=
1
(a, b) = 1
(
a
,
b
)
=
1
. Find
a
+
b
a + b
a
+
b
.
geometry