MathDB
Number of triangles in drawing

Source:

November 21, 2005

Problem Statement

Consider the figure consisting of a square, its diagonals, and the segments joining the midpoints of opposite sides. The total number of triangles of any size in the figure is
[asy] size(100); defaultpen(linewidth(0.7)); draw(unitsquare^^(0,0)--(1,1)^^(0,1)--(1,0)^^(.5,0)--(.5,1)^^(0,.5)--(1,.5));[/asy]
<spanclass=latexbold>(A)</span> 10<spanclass=latexbold>(B)</span> 12<spanclass=latexbold>(C)</span> 14<spanclass=latexbold>(D)</span> 16<spanclass=latexbold>(E)</span> 18<span class='latex-bold'>(A)</span>\ 10 \qquad <span class='latex-bold'>(B)</span>\ 12 \qquad <span class='latex-bold'>(C)</span>\ 14 \qquad <span class='latex-bold'>(D)</span>\ 16 \qquad <span class='latex-bold'>(E)</span>\ 18