So my problem is this: I need to figure out the center of a circle given two points. At one of the points, I know the tangent angle. So I know (x1, y1, θ1) and (x2, y2) and need to find (xc, yc). I also need to do this on a computer so I need some sort of closed-form solution.(adsbygoogle = window.adsbygoogle || []).push({});

The way I have approached this so far is to construct a line with the equation

x(t) = x1 + t*cos(θ+pi/2)

y(t) = y1 + t*sin (θ+pi/2)

This line runs through (x1,y1) as well as (xc, yc). There is some value of t (equal to + or - the radius of the circle) where (x(t),y(t)) = (xc,yc). Given that center of the circle is equidistant to both (x1,y1) and (x2,y2), I equate the squared distances:

[x(t)-x1]^2 + [y(t)-y1]^2 = [x(t)-x2]^2 + [y(t)-y2]^2

I substitute in equations for x(t) and y(t) and use a CAS to solve for t, although I come up with an extremely long, convoluted expression.

I have the feeling that there's got to be a simple, elegant way to do this, although I'm just not seeing it. Can anyone provide some insight or suggestions on how to approach this?

Thanks!

**Physics Forums - The Fusion of Science and Community**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Center of circle from two points and a tangent angle

Loading...

Similar Threads - Center circle points | Date |
---|---|

Jacobian for CoM coordinates | Nov 18, 2014 |

Question about the E-field along center axis of charged ring | Feb 7, 2014 |

Decide the center of mass | Mar 11, 2013 |

Finding the Center and Radius of a circle | Feb 17, 2009 |

A center of a circle with a parabola | Nov 22, 2007 |

**Physics Forums - The Fusion of Science and Community**