MathDB
Maximum number of regions

Source: 1971 AHSME Problem 17

April 20, 2014
geometryAMC

Problem Statement

A circular disk is divided by 2n2n equally spaced radii(n>0n>0) and one secant line. The maximum number of non-overlapping areas into which the disk can be divided is
<spanclass=latexbold>(A)</span>2n+1<spanclass=latexbold>(B)</span>2n+2<spanclass=latexbold>(C)</span>3n1<spanclass=latexbold>(D)</span>3n<spanclass=latexbold>(E)</span>3n+1<span class='latex-bold'>(A) </span>2n+1\qquad<span class='latex-bold'>(B) </span>2n+2\qquad<span class='latex-bold'>(C) </span>3n-1\qquad<span class='latex-bold'>(D) </span>3n\qquad <span class='latex-bold'>(E) </span>3n+1