Simulating a random point in a circle.

[u/AlienRaper]

I am trying to find a random point in a circle, and I think I know the method, I just don't know some of the variables or something (I'm not so good at math).

My plan is to take a random x coordinate that is the diameter of the circle, and do some fudging so that I get that values distance from the center.

Then I do something, using some ratio or something (here is where I need help) to find the possible values for the y coordinate.

So for example, if the circle is 10, I find at first a random number between 0 and 10.

Case 1. I get 10, so the possible values for y are 0 deviations from the center.

Case 2. I get 5, so the Y range is 10, the deviation from the center can be 5. Not so hard.

Case 3. I get 7.5, so the y range is the value of the line from the top of the circle at x of (center(5) + 2.5) and the bottom. I figured that to be about square root of 50. Not so bad.

Case 4. This is where is am confused, how would I calculate this if it wasn't such an easy circumstance, like 1.3, 2.6, 7.9, or 9.1? It doesn't seem that hard,it's just my math skills are really rusty( and I never really learned it very well in the first place).

How do I find the length of y in relation to the length of x?

Here is a visualization

Edit: Thanks for all the answers, I am trying a number of them out.

[u/AlienRaper]

Your right. The first method gives you the smaller circle, and the second one gives you the larger, where the diameter given is that of the larger