MathDB

\triangle ABC

points

D

and

E

lie on

\overline{BC}

and

\overline{AC}

, respectively. If

\overline{AD}

and

\overline{BE}

intersect at

T

so that AT/DT \equal{} 3 and BT/ET \equal{} 4, what is

CD/BD

? [asy]unitsize(2cm); defaultpen(linewidth(.8pt));
pair A = (0,0); pair C = (2,0); pair B = dir(57.5)*2; pair E = waypoint(C--A,0.25); pair D = waypoint(C--B,0.25); pair T = intersectionpoint(D--A,E--B);
label("

B

",B,NW);label("

A

",A,SW);label("

C

",C,SE);label("

D

",D,NE);label("

E

",E,S);label("

T

",T,2*W+N);
draw(A--B--C--cycle); draw(A--D); draw(B--E);[/asy]

<span class='latex-bold'>(A)</span>\ \frac {1}{8}\qquad <span class='latex-bold'>(B)</span>\ \frac {2}{9}\qquad <span class='latex-bold'>(C)</span>\ \frac {3}{10}\qquad <span class='latex-bold'>(D)</span>\ \frac {4}{11}\qquad <span class='latex-bold'>(E)</span>\ \frac {5}{12}

Problem Statement