# Perpendicular distance from chord to circle

I need to find the perpendicular distance from a chord to the circle, at arbitrary distance along the chord. I found an approximation using versine, but is there an exact formula?

Thanks Kevin

The perpendicular distance, if I understand this correctly, is just the distance from the point to the circle, along the radius. So given a cord, and a point on it, you can calculate the $$x$$ and $$y$$ positions of the point in terms of the distance from one end. Then the distance between that point and the circle is just $$R-\sqrt{x^2+y^2}$$. You would need to give more information about how you define the cord, in order to get a better answer.

Let a unit circle

$$x^2+y^2=1$$

and a horizontal chord

$$y=h.$$

The vertical distance is given by

$$y-h=\sqrt{1-x^2}-h,$$ for $$x$$ in $$\left[-\sqrt{1-h^2},\sqrt{1-h^2}\right].$$

• Thanks ! That's it.In my case, I know the length of cord, from which I can determine h from actual radius. – KevinM Feb 28 '19 at 18:37