Find the coordinates of a point on a circle without knowing the center point.

  1. Given 2 points on a circle, call them A and B. I know the cartesian coordinates of A. I also know the radius of the circle, the slope of the tangent line at A, and the length and direction of the arc between A and B. I don't know the coordiates of the center of the circle.

    How do I find the coordinates of point B?
  2. jcsd
  3. mathman

    mathman 6,706
    Science Advisor
    Gold Member

    The radius at A is perpendicular to the tangent line. The center is along the radius at a known distance. There are only two possible points. Use the information about B (direction of arc??) to choose the location of the center.
  4. Thanks mathman. I just needed a little insight, and you have provided that quickly and succinctly.
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