An Obtuse Viewing Angle
Let A = (0, 0) and B = (1, 0) be the bottom corners of the unit square [0, 1] × [0, 1]. A point P is chosen uniformly at random inside the square. What is the probability that the angle APB is obtuse (greater than 90°)? Give an exact closed form, or a decimal rounded to 4 places.
Related problems
Source: Classic geometric-probability exercise in wide circulation; no traceable original source. Statement written for AxiomIQ.