Resolved (Geometry) Length of a line where it goes through a circle.

hi. i need to find length of a line where goes through a circle with radius 690 meters. look at the picture to better understand what am i asking. thanks.


or how can i calculate distance from green sphere to point where line intersects with edge of purple circle.

 

Alright, let's dust off some high school algebra! The two important input numbers are: how far from the circle's center is the line (d), and how big is the circle's radius (r)? I see 690 here for the latter, and the former could be found with something like this sample code.

Obviously, if d > r, return 0. If d == 0, return r * 2. All other answers will be in between.

When you have the line reduced to "distance from the circle center", you can picture the problem as a horizontal line a=d units above the origin, so its formula is a simple y = d. If you can find the appropriate X where this line intersects the circle, you can multiply that by 2 and there's your length. The circle's formula is x^2 + y^2 = r^2.

So now you can just sort of mash the line's formula in with the circle's formula and solve for x.

x^2 + y^2 = r^2
y = d
x^2 + d^2 = r^2
x^2 = r^2 - d^2
x = sqrt(r^2 - d^2)

Multiply by 2 and there's your formula. Set r to 690 and d to your line's distance and you should get the right answer. Or in code form:

Code (csharp):

1. float GetDistWithinCircle(float lineDistToCircleCenter, float circleRadius) {
2. if (lineDistToCircleCenter >= circleRadius) return 0f; //if we don't do this one special we'll be taking sqrt of a negative number below
3. return 2f * Mathf.Sqrt(circleRadius * circleRadius - lineDistToCircleCenter * lineDistToCircleCenter);