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2007 Harvard-MIT Mathematics Tournament
11
11
Part of
2007 Harvard-MIT Mathematics Tournament
Problems
(1)
2007 Guts #11: Two Circles in a Plane
Source:
6/22/2012
Let
A
10
A_{10}
A
10
denote the answer to problem
10
10
10
. Two circles lie in the plane; denote the lengths of the internal and external tangents between these two circles by
x
x
x
and
y
y
y
, respectively. Given that the product of the radii of these two circles is
15
/
2
15/2
15/2
, and that the distance between their centers is
A
10
A_{10}
A
10
, determine
y
2
−
x
2
y^2-x^2
y
2
−
x
2
.