MathDB

Brocard Point

Source:

December 18, 2005

AMCAIMEtrigonometrygeometrynumber theoryrelatively primetrig identities

Problem Statement

Point

P

is located inside traingle

ABC

so that angles

PAB, PBC,

and

PCA

are all congruent. The sides of the triangle have lengths

AB=13, BC=14,

and

CA=15,

and the tangent of angle

PAB

m/n,

where

m

and

n

are relatively prime positive integers. Find

m+n.