MathDB
Interior Triangles

Source: AMC 10 2010A Problem 22

February 10, 2010
AMC

Problem Statement

Eight points are chosen on a circle, and chords are drawn connecting every pair of points. No three chords intersect in a single point inside the circle. How many triangles with all three vertices in the interior of the circle are created? <spanclass=latexbold>(A)</span> 28<spanclass=latexbold>(B)</span> 56<spanclass=latexbold>(C)</span> 70<spanclass=latexbold>(D)</span> 84<spanclass=latexbold>(E)</span> 140 <span class='latex-bold'>(A)</span>\ 28 \qquad <span class='latex-bold'>(B)</span>\ 56 \qquad <span class='latex-bold'>(C)</span>\ 70 \qquad <span class='latex-bold'>(D)</span>\ 84 \qquad <span class='latex-bold'>(E)</span>\ 140