MathDB
1990 AHSME #4: Parallelogram

Source:

January 1, 2013
geometryparallelogramAMC

Problem Statement

Let ABCDABCD be a parallelogram with ABC=120\angle ABC=120^\circ, AB=16AB=16 and BC=10BC=10. Extend CD\overline{CD} through DD to EE so that DE=4DE=4. If BE\overline{BE} intersects AD\overline{AD} at FF, then FDFD is closest to
<spanclass=latexbold>(A)</span>1<spanclass=latexbold>(B)</span>2<spanclass=latexbold>(C)</span>3<spanclass=latexbold>(D)</span>4<spanclass=latexbold>(E)</span>5<span class='latex-bold'>(A) </span>1\qquad <span class='latex-bold'>(B) </span>2\qquad <span class='latex-bold'>(C) </span>3\qquad <span class='latex-bold'>(D) </span>4\qquad <span class='latex-bold'>(E) </span>5
[asy] size(200); defaultpen(linewidth(0.8)); pair A=origin,B=(16,0),C=(26,10*sqrt(3)),D=(10,10*sqrt(3)),E=(0,10*sqrt(3)); draw(A--B--C--E--B--A--D); label("AA",A,S); label("BB",B,S); label("CC",C,N); label("DD",D,N); label("EE",E,N); label("FF",extension(A,D,B,E),W); label("44",(D+E)/2,N); label("1616",(8,0),S); label("1010",(B+C)/2,SE); [/asy]