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Math Help - Finding the center of a circle

  1. #1
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    Finding the center of a circle

    Given
    1)A point A(x,y).
    2)Two others points P(x1,y1) and Q(x2,y2)

    Find
    The equation(basically the center) of circle that is tangent to line AP and AQ and of given radius r.

    How to solve it.
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  2. #2
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    Quote Originally Posted by gunjannigam View Post
    Given
    1)A point A(x,y).
    2)Two others points P(x1,y1) and Q(x2,y2)

    Find
    The equation(basically the center) of circle that is tangent to line AP and AQ and of given radius r.

    How to solve it.
    1. The 3 points should not be placed on one single straight line.

    2. Let M\left(x_M,\ y_M\right) be the midpoint of the circle. The distance of M to AP or AQ must be |r|.

    3. Consequently you get 4 pairs of equations for the 4 different Ms:

    d(M, AP) = r~\wedge~d(M, AQ) = r

    d(M, AP) = r~\wedge~d(M, AQ) = -r

    d(M, AP) = -r~\wedge~d(M, AQ) = r

    d(M, AP) = -r~\wedge~d(M, AQ) = -r

    4. Solve each pair of equations for \left(x_M,\ y_M\right)
    Attached Thumbnails Attached Thumbnails Finding the center of a circle-vierkreis_tang.png  
    Last edited by earboth; December 2nd 2009 at 10:18 PM.
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