# Calculating four points on a circle

• Feb 22nd 2010, 09:28 AM
sesproul
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
• Feb 22nd 2010, 10:19 AM
bjhopper
Quote:

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.
• Feb 22nd 2010, 10:36 AM
sesproul
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
• Feb 22nd 2010, 10:56 AM
Diagonal
Quote:

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.