Distance between 2 points

[Mr. Neo]

I seem to be having a bit of a problem on this math problem, perhaps one of you math wizards could shed some insight into my problem?

Let's say that I have a circle shaped figure and I have a list of points that are defined on the outer rim of this figure.  How would I go about taking two points and find the distance inbetween them?  This would be similar to how you use the Pythagorean Theorem to find the distance between two points on a right triangle.  Is there an equation similar to this that works with a circle?

Thanks,

[Yoni]

By "distance" you mean the length of the circle's circumference between the 2 points?

[Mr. Neo]

Yes.

[Yoni]

Aha. I will post the solution within 24 hours if someone else doesn't.

Edit: Actually it's simpler than I thought. Don't wait 24 hours. Here is a walkthrough:

1. Name the given 2 points "A" and "B", and name the center of the circle "O". The length of the radius is R.
2. Find the angle <AOB in RADIANS.
3. The solution is: R * <AOB

That's it

Justification: Think about it. The entire circumference is R * 2pi. 2pi is a central angle that covers the entire circle. So an angle that covers only "alpha" would be R * alpha.

[Mr. Neo]

Thank you very much Yoni, it works perfectly. 

[TheMinistered]

Well, yoni's example seems a bit overcomplicated-- just use the distance formula.

Distance = SquareRoot( (x2 - x1)^2 + (y2 - y1)^2 )


However, I'm assuming you didn't mean a straight line, but rather the distance between the two points traveling along the edge of the circle.

[j0k3r]

If you're assuming he meant the distance around the edge, why did you leave your solution? Also, what if the circle doesn't lie on a cartesian plane? Your solution is relying on two points with values, while Yoni's requires only the radius and two points no matter what their value.

[dxoigmn]

What about a formula for the distance between 2 points on a conic section with a given eccentricity?  (for a circle, eccentricity = 0)