MathDB
1993 AMC 12 #17 - Painted Dartboard

Source:

January 2, 2012
geometryratioAMC

Problem Statement

Amy painted a dart board over a square clock face using the "hour positions" as boundaries. [See figure.] If tt is the area of one of the eight triangular regions such as that between 1212 o'clock and 11 o'clock, and qq is the area of one of the four corner quadrilaterals such as that between 11 o'clock and 22 o'clock, then qt=\frac{q}{t}= [asy] size((80)); draw((0,0)--(4,0)--(4,4)--(0,4)--(0,0)--(.9,0)--(3.1,4)--(.9,4)--(3.1,0)--(2,0)--(2,4)); draw((0,3.1)--(4,.9)--(4,3.1)--(0,.9)--(0,2)--(4,2)); [/asy] <spanclass=latexbold>(A)</span> 232<spanclass=latexbold>(B)</span> 32<spanclass=latexbold>(C)</span> 5+12<spanclass=latexbold>(D)</span> 3<spanclass=latexbold>(E)</span> 2 <span class='latex-bold'>(A)</span>\ 2\sqrt{3}-2 \qquad<span class='latex-bold'>(B)</span>\ \frac{3}{2} \qquad<span class='latex-bold'>(C)</span>\ \frac{\sqrt{5}+1}{2} \qquad<span class='latex-bold'>(D)</span>\ \sqrt{3} \qquad<span class='latex-bold'>(E)</span>\ 2