Mock AIME 1 2013 Problems
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Contents
Problem 1
Two circles and
, each of unit radius, have centers
and
such that
. Let
be the midpoint of
and let $C_#$ (Error compiling LaTeX. Unknown error_msg) be a circle externally tangent to both
and
.
and
have a common tangent that passes through
. If this tangent is also a common tangent to
and
, find the radius of circle
.
Problem 2
Find the number of ordered positive integer pairs such that
evenly divides
,
evenly divides
, and
.
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10