# Thread: Calculating four points on a circle

1. ## Calculating four points on a circle

Hello,

I have a tricky problem, and it has been years since Geometry.

I need to calculate the points on and inner and outer circle based on a center line and a known Chord Length (L) and two know Radius (A, B)

I am trying to locate A1, A2 and B1, B2

Here is a diagram to help explain.

Thanks

Steve

2. Originally Posted by sesproul
Hello,

I have a tricky problem, and it has been years since Geometry.

I need to calculate the points on and inner and outer circle based on a center line and a known Chord Length (L) and two know Radius (A, B)

I am trying to locate A1, A2 and B1, B2

Here is a diagram to help explain.

Thanks

Steve
Use analytic geometry treating each circle separately where both circles are centered @ 0,0.

3. I belive that I determines the solution using that method. Where I calc the Angle of Chord A (Div 2 using A and L) and Arc Sine, and then use that angle to calculate the hight of "Y" point using the Cosine of the angle, and A.

Thanks

Steve

4. Originally Posted by sesproul
Hello,

I have a tricky problem, and it has been years since Geometry.

I need to calculate the points on and inner and outer circle based on a center line and a known Chord Length (L) and two know Radius (A, B)

I am trying to locate A1, A2 and B1, B2

Here is a diagram to help explain.

Thanks

Steve
Do you want coordinate (x,y) values for a circle centered at the origin? Or, do you want some ordinary (Euclidean) geometry construction? If the first, I'd use symmetry to advantage [Same above as below and as left is to right, so having found one, the rest follow form equal distances] If the second, I'd use a simple drafting program.

For the first, a circle of radius "r", centered at the origin has an equation x^2 + y^2 = r^2 The chord is divided equally above and below the x-axis, so the distance to A1 for example would be L/2, where L is the length of the chord. That is the y-value. Sub that into the value for y and you have x^2 = r^2 - (L/2)^2 from which you can find the x-value.

For the second, the only change is the radius length. If the first is r, the second could be R.