Your sketch works fine, but I don't understand what your problem is. Can you be more concrete? What segments? What length? Etc.

hi, the four arcs within ellipse, i want to limit the extent to which they extend beyond the radius of the ellipse (ideally max twice the radius).

In your code example the last lines could be changed to this...

1.     float rad2 = dist(0, 0, mx, my)*2;
2.     rad2 = constrain(rad2,0,rad*2);
3.     fill(colors[ind]);
4.     arc(0, 0, rad2, rad2, ang[ind][0], ang[ind][1]);

However let me also give an alternative way of doing the whole thing...

1. int radius = 120;
2. color arcColor;
3. int angle;
4.  
5. void setup() {
6.   size(500, 500);
7.   strokeWeight(2);
8.   smooth();
9. }
10.  
11. void draw () {
12.   background(255);
13.   translate(width/2, height/2);
14.  
15.   fill(230);
16.   ellipse(0, 0, radius, radius);
17.  
18.   if (mousePressed) {
19.     drawArcs();
20.   }
21. }
22. void drawArcs() {
23.   float distance = dist(mouseX, mouseY, width/2, height/2);
24.   distance = min(distance, radius);
25.  
26.   if (mouseY>height/2) {
27.     if (mouseX<width/2) {
28.       angle = 90;
29.       arcColor = color(0, 0, 255, 140);
30.     } else {
31.       angle = 0;
32.       arcColor = color(255, 0, 0, 140);
33.     }
34.   } else {
35.     if (mouseX<width/2) {
36.       angle = 180;
37.       arcColor = color(80, 0, 105, 140);
38.     } else {
39.       angle = 270;
40.       arcColor = color(0, 220, 0, 140);
41.     }
42.   }
43.  
44.   fill(arcColor);
45.   arc(0, 0, distance*2, distance*2, radians(angle), radians(angle+90));
46. }