MathDB

Let

ABC

be a triangle with

AB=5

BC=7

CA=8

, and circumcircle

\omega

. Let

P

be a point inside

ABC

such that

PA:PB:PC=2:3:6

. Let rays

\overrightarrow{AP}

\overrightarrow{BP}

, and

\overrightarrow{CP}

intersect

\omega

again at

X

Y

, and

Z

, respectively. The area of

XYZ

can be expressed in the form

\dfrac{p\sqrt q}{r}

where

p

and

r

are relatively prime positive integers and

q

is a positive integer not divisible by the square of any prime. What is

p+q+r

?
Proposed by James Lin

Problem Statement