MathDB
Bored Isabella

Source: 2015 AMC 12A #11

February 4, 2015
AMC

Problem Statement

On a sheet of paper, Isabella draws a circle of radius 22, a circle of radius 33, and all possible lines simultaneously tangent to both circles. Isabella notices that she has drawn exactly k0k\geq 0 lines. How many different values of kk are possible?
<spanclass=latexbold>(A)</span>2<spanclass=latexbold>(B)</span>3<spanclass=latexbold>(C)</span>4<spanclass=latexbold>(D)</span>5<spanclass=latexbold>(E)</span>6<span class='latex-bold'>(A) </span>2\qquad<span class='latex-bold'>(B) </span>3\qquad<span class='latex-bold'>(C) </span>4\qquad<span class='latex-bold'>(D) </span>5\qquad<span class='latex-bold'>(E) </span>6