TurtleGraphics Python - Constraining random-moving turtle in a circle?

Question

How would I be able to make a randomly moving turtle be constrained inside a circle with a radius of 50, the circles center being at (0, 0)? So if the turtle is currently at location (x, y), it's distance from the center is math.sqrt(x ** 2 + y ** 2). Whenever the turtle's distance from the center is more than 50, have it turn around and continue. I have gotten the code to work with the screen size, but where do I put math.sqrt(x ** 2 + y ** 2) to get it to be constrained in a circle? Here's the code I have so far:

import turtle, random, math

def bounded_random_walk(num_steps, step_size, max_turn):
    turtle.reset()
    width = turtle.window_width()
    height = turtle.window_height()
    for step in range(num_steps):
       turtle.forward(step_size)
       turn = random.randint(-max_turn, max_turn)
       turtle.left(turn)

       x, y = turtle.position()
       if -width/2 <= x <= width/2 and -height/2 <= y <= height/2:
           pass
       else:  # turn around!
           turtle.left(180)
           turtle.forward(step_size)

This code works for a turtle in the screen, but not in a circle.

Answer 1

Where you're coding:

   if -width/2 <= x <= width/2 and -height/2 <= y <= height/2:

you really mean "if point(x, y) is inside the permitted area". So, when "the permitted area" is "a circle with radius 50 centered at origin", comparing the squares of distances and radius (it's clearer than taking square roots...!-) you'd have:

   if (x*x + y*y) <= 50*50:

leaving all the rest of your code unchanged.

Edit: since the OP commented that this doesn't work for him I changed the if/else to:

   x, y = turtle.position()
   # if -width/3 <= x <= width/3 and -height/3 <= y <= height/3:
   if (x*x + y*y) <= 50*50:
       pass
   else:  # turn around!
       print 'Bounce', step, x, y
       turtle.left(180)
       turtle.forward(step_size)

and ran it as bounded_random_walk(200, 10, 30) from a Terminal.App on Mac OS X so the print would show. The result is I get about 50 to 60 prints of "Bounce" and the turtle clearly IS being bounded inside the desired circle, as logic and geometry also say it must.

So I hope the OP will edit their own answer along these lines (ideally on a system and in an arrangement where he can see the results of print or some other way of giving output and ideally show them to us) so that I can help him debug his code.