MathDB

Point

P

is inside

\triangle ABC

. Line segments

APD

BPE

, and

CPF

are drawn with

D

BC

E

AC

, and

F

AB

(see the figure at right). Given that

AP=6

BP=9

PD=6

PE=3

, and

CF=20

, find the area of

\triangle ABC

.
[asy] size(200); pair A=origin, B=(7,0), C=(3.2,15), D=midpoint(B--C), F=(3,0), P=intersectionpoint(C--F, A--D), ex=B+40*dir(B--P), E=intersectionpoint(B--ex, A--C); draw(A--B--C--A--D^^C--F^^B--E); pair point=P; label("

A

", A, dir(point--A)); label("

B

", B, dir(point--B)); label("

C

", C, dir(point--C)); label("

D

", D, dir(point--D)); label("

E

", E, dir(point--E)); label("

F

", F, dir(point--F)); label("

P

", P, dir(0));[/asy]

Problem Statement