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BodhiAI1
Nov. 13, 2019

Radical Axis ,Center:

Radical Axis

The radical axis of two circles is the locus of a point which moves such that the lengths of the tangents drawn from it to the two circles are equal.

Equation of Radical Axis

Let and

Now, According to definition of Radical Axis, we have

Squaring both sides, we get

Locus of

which is the required equation of the radical axis of the given circles.

 


 

Radical Centre

The radical axes of three circles, taken in pairs, meet in a point, which is called their radical centre

Reasoning: Let and be the equations of circles. If OL, OM and ON are the radical axes with respect to the pair of circles and . respectively, then the equations of lines OL, OM and ON are given by

Now, let the lines OL and OM intersect in O, then according to the condition of family of lines, the equation of line through the point of intersection of lines is given by 

where, is any constant

Hence the radical axis of three circles are concurrent and that point of concurrency is called Radical Centre.