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Math Help - find points on a circle

  1. #1
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    find points on a circle

    If I know the coordinates of the centre of a circle and its radius, how do I find other points on the circle?

    (-not including the perfect "north,south,east,west positions")

    (-not using simple trig: [sin theta * r] and [cos theta * r], then add those to x,y of centre)

    TYIA
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  2. #2
    Super Member
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    Quote Originally Posted by hello View Post
    If I know the coordinates of the centre of a circle and its radius, how do I find other points on the circle?

    (-not using simple trig: [sin theta * r] and [cos theta * r]...

    Center of circle at (a,b)

    Given an arbitrary x coordinate, need to find y:

    r^2 = (x-a)^2 + (y-b)^2
    x^2 -2xa + a^2 = (y-b)^2 - r^2

    The LHS contains the unknown.
    x^2 -2xa - (y-b)^2 + r^2 + a^2 = 0
    Solve the quadratic.
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