Radical axis and centre

Radical axis

Radical axis is a locus of a point from which length of tangent to two circles are equal. 


In case of concentric circles radical axis does not exist. 

If S ≡ x² + y² + 2gx + 2fy + c

   S’ ≡ x² + y² + 2g’x + 2f’y+ c’

Then equation of radical axis of two circles.

S = 0 and S’ = 0 is given by S = S’

x² + y² + 2gx + 2fy + c = x² + y² + 2g’x + 2f’y + c’

2(g – g’)x + 2(f – f’)y + (c – c’) = 0


Radical centre

Radical axis is always perpendicular to the line joining centres of the circle. 

Radical axis of three circles whose centres are (non-collinear) taken in pair are always concurrency is called radical centre. 

Radical centre is a point from which length of tangent to all three circles are equal. 

Taking radical centre as centre and length of tangent equal to radius if we draw a circle then this circle is orthogonal to all three given circles. 
Provided that radical centre lies outside the circle. 



*For high school studies

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