Refer to the picture below, my problem/questions will follow

I have two points, one is the center of the circle and one is a point on the circumference of the circle.

What I need to do is find the position of points A, B, C and D given that the arc length between each points is 10

I'm trying to find the best method (least computational) way of doing this.

I have found a way that requires essentially 3 steps (which I will detail below) but I believe there is a better solution.

my solution:

Step 1 - Use the Arc Length equation to solve for the central angle C, we have the arc length (10) and we can get the radius r

Step 2 - Use the Arctangent function to obtain the angle of the known point on the circle's circumference in relation to the center point

Step 3 - Subtract the central angle found in Step 1 from the angle found in Step 2 and plot a point on the circle's circumference at this angle with a distance of the radius (also found in Step 1)

This works, but is a lot of math. I would think there is a more simple way to do this... does anyone have an idea?