MathDB

Let

ABCD

be a unit square in the plane. Points

X

and

Y

are chosen independently and uniformly at random on the perimeter of

ABCD

. If the expected value of the area of triangle

\triangle AXY

can be expressed as

\frac{m}{n}

for relatively prime positive integers

m

and

n

, compute

m+n

.
Proposed by Nathan Xiong

Problem Statement