MathDB

\triangle ABC,

a point

E

is on

\overline{AB}

with

AE=1

and

EB=2.

Point

D

is on

\overline{AC}

so that

\overline{DE} \parallel \overline{BC}

and point

F

is on

\overline{BC}

so that

\overline{EF} \parallel \overline{AC}.

What is the ratio of the area of

CDEF

to the area of

\triangle ABC?

[asy] size(7cm); pair A,B,C,DD,EE,FF; A = (0,0); B = (3,0); C = (0.5,2.5); EE = (1,0); DD = intersectionpoint(A--C,EE--EE+(C-B)); FF = intersectionpoint(B--C,EE--EE+(C-A)); draw(A--B--C--A--DD--EE--FF,black+1bp); label("

A

",A,S); label("

B

",B,S); label("

C

",C,N); label("

D

",DD,W); label("

E

",EE,S); label("

F

",FF,NE); label("

1

",(A+EE)/2,S); label("

2

",(EE+B)/2,S); [/asy]

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

Problem Statement