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Math Help - [SOLVED] Center of a circle tangent to other two circles

  1. #1
    Helder Barros
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    [SOLVED] Center of a circle tangent to other two circles

    I need to find the center circle with a radius R3, tangent to other two circles with radius R1 and R2 and centers X1, Y1 and X2,Y2.

    Any help? Thanks in avance!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Helder Barros
    I need to find the center circle with a radius R3, tangent to other two circles with radius R1 and R2 and centers X1, Y1 and X2,Y2.

    Any help? Thanks in avance!
    The centre of the required circle is at a distance of R_1+R_3
    from (X_1,Y_1), and also at a distance of R_2+R_3 from (X_2,Y_2).

    Hence the centre is at the point of intersection of:

    (x-X_1)^2\ +\ (y-Y_1)^2\ =\ (R_1+R_3)^2

    and

    (x-X_2)^2\ +\ (y-Y_2)^2\ =\ (R_2+R_3)^2

    (note there can be zero one or two solutions to this, also this
    is for exterior tangency, if R_3 is large enough we
    can also have interior tangency which would require a change to
    the RHS of the equations to (R_3-R_1)^2 and (R_3-R_2)^2 respectivly.
    Now I think of it you can also have mixed interior
    and exterior tangency)

    RonL
    Attached Thumbnails Attached Thumbnails [SOLVED] Center of a circle tangent to other two circles-circles.png  
    Last edited by CaptainBlack; December 9th 2005 at 05:22 AM.
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