+193 We can place the diagram in the coordinate plane so that A = (0,s), B = (0,0), C = (s,0), and D = (s,s), where s is the side length of the square. Let P = (x,y). Then
x^2 + (y - s)^2 = 1
x^2 + y^2 = 4
(x - s)^2 + y^2 = 9
Solving, we get s = 2 + sqrt(3), x = sqrt(3)/4, y = 1/2 + sqrt(3)/8. Then by the cosine law, angle APB = 120 degrees.
