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2020 LMT Spring
10
10
Part of
2020 LMT Spring
Problems
(1)
Spring 2020 Team Round Problem 10
Source:
8/22/2020
Three mutually externally tangent circles are internally tangent to a circle with radius
1
1
1
. If two of the inner circles have radius
1
3
\frac{1}{3}
3
1
, the largest possible radius of the third inner circle can be expressed in the form
a
+
b
c
d
\frac{a+b\sqrt{c}}{d}
d
a
+
b
c
where
c
c
c
is squarefree and
gcd
(
a
,
b
,
d
)
=
1
\gcd(a,b,d)=1
g
cd
(
a
,
b
,
d
)
=
1
. Find
a
+
b
+
c
+
d
a+b+c+d
a
+
b
+
c
+
d
.