MathDB

Rectangle and parallel lines

Source:

March 18, 2011

geometryrectangleLaTeXratioAMCAIMEAoPSwiki

Problem Statement

In rectangle

ABCD

,

AB=12

and

BC=10

. Points

E

and

F

lie inside rectangle

ABCD

so that

BE=9

,

DF=8

,

\overline{BE} \parallel \overline{DF}

,

\overline{EF} \parallel \overline{AB}

, and line

BE

intersects segment

\overline{AD}

. The length

EF

can be expressed in the form

m\sqrt{n}-p

, where

m,n,

and

p

are positive integers and

n

is not divisible by the square of any prime. Find

m+n+p

.

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