Find the new bisector length form a moved circle chord?

Question

I have no idea if this is the right forum to ask, but it is a math question. Please let me know where to ask if this is wrong. Sorry.

I have a chord going through a circle and know the length from that chord to the edge of the circle. If I move that chord "up", I need to know how to calculate the new "length" from the chord to the edge of the circle.

I've added an image (I hope it worked)

It's a less common trigonometric function these days, but that length has a name: versine. — Sammy Black, Jun 29 '22 at 22:24
Move this "chord" up... by how much? The new length is obviously different if you move the chord up by a different amount. — peterwhy, Jun 29 '22 at 23:33

score 1 · Answer 1 · answered Jun 29 '22 at 22:21

1

It's simple Pythagoras. If the radius of the circle $(r)$ is known, and the distance from the origin to the chord is known $(h)$, then the length of the chord $(c)$ can be gotten from $\frac{c}{2} = \sqrt{r^2-h^2}$, or $c = 2\sqrt{r^2-h^2}$.

answered Jun 29 '22 at 22:21

Daniel P

2,710

Unfortunately, I don't have the radius or know the dostsnce of origin to the chord. – KeepCool Jun 29 '22 at 22:37

Find the new bisector length form a moved circle chord?

1 Answers1