Mock AIME 1 2013 Problems
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 . Solution
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10