MathDB

In triangle

ABC

, AC \equal{} 13, BC \equal{} 14, and AB\equal{}15. Points

M

and

D

lie on

AC

with AM\equal{}MC and \angle ABD \equal{} \angle DBC. Points

N

and

E

lie on

AB

with AN\equal{}NB and \angle ACE \equal{} \angle ECB. Let

P

be the point, other than

A

, of intersection of the circumcircles of

\triangle AMN

and

\triangle ADE

. Ray

AP

meets

BC

Q

. The ratio

\frac{BQ}{CQ}

can be written in the form

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. Find m\minus{}n.

Problem Statement