radical axis

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The radical axis of two circles is the straight line containing all points P such that the lengths of the tangents from P to the two circles are equal. Each figure below shows a point P on the radical axis and tangents touching the two circles at T1 and T2, with PT1=PT2. If the circles intersect in two points, as in the figure on the right, the radical axis is the straight line through the two points of intersection. In this case, there are some points on the radical axis inside the circles, from which tangents to the two circles cannot be drawn. For the circles with equations x2+y2+2g1x+2f1y+c1=0 and x2+y2+2g2x+2f2y+c2=0, the radical axis has equation 2(g1g2)x+2(f1f2)y+(c1c2)=0.

Subjects: Mathematics.

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