MathDB

Aime 2005a #15

Source: Aime 2005a #15

November 10, 2005

AIMEgeometryquadraticsincenterarea of a triangleHeron's formula

Problem Statement

Triangle

ABC

has

BC=20

. The incircle of the triangle evenly trisects the median

AD

. If the area of the triangle is

m \sqrt{n}

where

m

and

n

are integers and

n

is not divisible by the square of a prime, find

m+n