How to generate random coordinates outside the circle contained in a rectangular region?

Question

Given:

1. Rectangular region with length l & breadth b
2. Circle with radius r
3. Circle is contained in rectangular region like shown in below image

See image here - Red are expecting evenly distributed coordinates

Then how to generate random coordinates outside the circle contained in a rectangular region and evenly distributed? (in blue region of below image)

Answer 1

Generate two random values in ranges (uniform distribution in rectangle)

a = Math.random() * width
b = Math.random() * height

check if point lies outside the circle:

(a-center_x)*(a-center_x)+(b-center_y)*(b-center_y) > r*r

if not - repeat random generation until condition becomes true (this is rejection method)

Generated by this Delphi code for reference

var
  Hgt, Wdt, i, N, CX, CY, R, x, y: Integer;
begin
  Hgt := 300;
  Wdt := 400;
  CX := 220;
  CY := 120;
  R := 100;
  N := 15000;
  for i := 0 to N-1 do begin
    x := Round(Random() * Wdt);
    y := Round(Random() * Hgt);
    while (x-CX)*(x-CX)+(y-CY)*(y-CY) < R*R do begin
      x := Round(Random() * Wdt);
      y := Round(Random() * Hgt);
    end;
    Canvas.Pixels[x, y] := clRed;
  end;