MathDB

Area of a Subtriangle

Source:

December 26, 2006

geometrycircumcircletrigonometrynumber theoryrelatively primetrig identitiesLaw of Cosines

Problem Statement

Triangle

ABC

is a right triangle with

AC=7,

BC=24,

and right angle at

C.

Point

M

is the midpoint of

AB,

and

D

is on the same side of line

AB

as

C

so that

AD=BD=15.

Given that the area of triangle

CDM

may be expressed as

\frac{m\sqrt{n}}{p},

where

m,

n,

and

p

are positive integers,

m

and

p

are relatively prime, and

n

is not divisible by the square of any prime, find

m+n+p.

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