MathDB
Find BE

Source: AHSME 1963 Problem 38

January 13, 2014
geometryparallelogramAsymptotesimilar trianglesAMC

Problem Statement

Point FF is taken on the extension of side ADAD of parallelogram ABCDABCD. BFBF intersects diagonal ACAC at EE and side DCDC at GG. If EF=32EF = 32 and GF=24GF = 24, then BEBE equals:
[asy] size(7cm); pair A = (0, 0), B = (7, 0), C = (10, 5), D = (3, 5), F = (5.7, 9.5); pair G = intersectionpoints(B--F, D--C)[0]; pair E = intersectionpoints(A--C, B--F)[0]; draw(A--D--C--B--cycle); draw(A--C); draw(D--F--B); label("AA", A, SW); label("BB", B, SE); label("CC", C, NE); label("DD", D, NW); label("FF", F, N); label("GG", G, NE); label("EE", E, SE); //Credit to MSTang for the asymptote [/asy]

<spanclass=latexbold>(A)</span> 4<spanclass=latexbold>(B)</span> 8<spanclass=latexbold>(C)</span> 10<spanclass=latexbold>(D)</span> 12<spanclass=latexbold>(E)</span> 16<span class='latex-bold'>(A)</span>\ 4 \qquad <span class='latex-bold'>(B)</span>\ 8\qquad <span class='latex-bold'>(C)</span>\ 10 \qquad <span class='latex-bold'>(D)</span>\ 12 \qquad <span class='latex-bold'>(E)</span>\ 16