Let θ = angle
APB
- If P is within the white region, the angle is acute. See P1.
- If P is on the red semi-circular curve, the angle is right. See P2.
- If P is inside the semi-circular area, the angle is obtuse. See P3.
$P = \dfrac{A_\text{semi-circle}}{A_\text{square}}$
$P = \dfrac{\frac{1}{2}\pi (0.5^2)}{1^2}$
$P = \pi / 8$ ← answer