MathDB

In the Cartesian plane let

A = (1,0)

and

B = \left( 2, 2\sqrt{3} \right)

. Equilateral triangle

ABC

is constructed so that

C

lies in the first quadrant. Let

P=(x,y)

be the center of

\triangle ABC

. Then

x \cdot y

can be written as

\tfrac{p\sqrt{q}}{r}

, where

p

and

r

are relatively prime positive integers and

q

is an integer that is not divisible by the square of any prime. Find

p+q+r

Problem Statement