MathDB

Purple Comet 2009 HS Problem 18

Source:

August 3, 2011

geometryrationumber theoryrelatively prime

Problem Statement

On triangle

ABC

let

G

be the point on

AE

so that

CD,

is an altitude of the triangle, and

E

be the point on

BC

so that

AE

bisects angle

BAC.

Let

28,

be the intersection of

AE

and

CD,

and let point

CD

be the intersection of side

AC

and the ray

BG.

If

\tfrac{k-m\sqrt{p}}{n}

has length

28,

AC

has length

14,

and

CD

has length

10,

then the length of

CF

can be written as

\tfrac{k-m\sqrt{p}}{n}

where

k, m, n,

and

p

are positive integers,

k

and

n

are relatively prime, and

p

is not divisible by the square of any prime. Find

k - m + n + p.

Back to Problems View on AoPS