define your circle using a centre and a radius.

pick your random point. it's inside if the distance from the centre to the point is less than the radius. (use dist())

perhaps better, pick a random radius between 0 and the radius of the circle. then pick a random angle between 0 and TWO_PI. use these as the polar coordinates for your random point. (use cos() and sin())

Thanks, that's a great help

or just use sin / cos and randomize alpha and the radius

1. /*
   *
   */
   
   void setup() {
     size(600,600);
     smooth();
     background(255);
   
   }
   
   void draw() {
    
   float radius = random(200);
   float a = random(TWO_PI);
   
   float x = width/2+cos(a )*radius;
   float y = height/2+sin( a )*radius;
   
   ellipse(x,y,3,3);
   
   
   }
   
   
    
   

Yet another (and approx. 25-30% faster) approach is based on the circle formula/pythagorean and doesn't need trigonometry:  radius =  x*x + y*y: