MathDB

Area Ratio in Triangle

Source:

December 28, 2006

geometryratioinequalitiesnumber theoryrelatively primetriangle inequality

Problem Statement

In triangle

ABC,

point

D

is on

\overline{BC}

with

CD=2

and

DB=5,

point

E

is on

\overline{AC}

with

CE=1

and

EA=3,

AB=8,

and

\overline{AD}

and

\overline{BE}

intersect at

P.

Points

Q

and

R

lie on

\overline{AB}

so that

PQR

is parallel to

\overline{CA}

and

\overline{PR}

is parallel to

\overline{CB}.

It is given that the ratio of the area of triangle

PQR

to the area of triangle

ABC

is

m/n,

where

m

and

n

are relatively prime positive integers. Find

m+n.

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