Solve the following math problem efficiently and clearly:

- For simple problems (2 steps or fewer):
Provide a concise solution with minimal explanation.

- For complex problems (3 steps or more):
Use this step-by-step format:

## Step 1: [Concise description]
[Brief explanation and calculations]

## Step 2: [Concise description]
[Brief explanation and calculations]

...

Regardless of the approach, always conclude with:

Therefore, the final answer is: $oxed{answer}$. I hope it is correct.

Where [answer] is just the final number or expression that solves the problem.

Problem: Let $ABC$ be a  triangle with $\angle BAC = 90^\circ$.  A circle is tangent to the sides $AB$ and $AC$ at $X$ and $Y$ respectively, such that the points on the circle diametrically opposite $X$ and $Y$ both lie on the side $BC$.  Given that $AB = 6$, find the area of the portion of the circle that lies outside the triangle.

[asy]
import olympiad;
import math;
import graph;

unitsize(4cm);

pair A = (0,0);
pair B = A + right;
pair C = A + up;

pair O = (1/3, 1/3);

pair Xprime = (1/3,2/3);
pair Yprime = (2/3,1/3);

fill(Arc(O,1/3,0,90)--Xprime--Yprime--cycle,0.7*white);

draw(A--B--C--cycle);
draw(Circle(O, 1/3));
draw((0,1/3)--(2/3,1/3));
draw((1/3,0)--(1/3,2/3));

draw((1/16,0)--(1/16,1/16)--(0,1/16));

label("$A$",A, SW);
label("$B$",B, down);
label("$C$",C, left);
label("$X$",(1/3,0), down);
label("$Y$",(0,1/3), left);

[/asy]
user