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By subtraction of the two given equations one gets the line equation:
:This special line is the radical line of the two circles.Special case :
In this case the origin is the center of the first circle and the second center lies on the x-axis (s. diagram). The equation of the radical line simplifies to and the points of intersection can be written as with
:In case of the circles have no points in common.
In case of the circles have one point in common and the radical line is a common tangent.

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