Question 444149
Upon drawing the diagram, you will see that


*[tex \LARGE r_A + r_B = 7]

*[tex \LARGE r_B + r_C = 10]

*[tex \LARGE r_C + r_A = 11]


where *[tex r_A] is the radius of circle A. Using any method to solve the system (preferably adding all three equations to find the sum of the radii), we obtain

*[tex \LARGE  r_A = 4]

*[tex \LARGE r_B = 3]

*[tex \LARGE r_C = 7]


Hence, the radius of circle C is largest.