Geo4.116

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Find the radical centre of the circles x^{2}+y^{2}=9,x^{2}+y^{2}-2x-2y-5=0,x^{2}+y^{2}+4x+6y-19=0\,

The radical axis of the first two circles is

(x^{2}+y^{2}-9)-(x^{2}+y^{2}-2x-2y-5)=0\,

2x+2y-4=0,x+y-2=0\,

The radical axis of the second and third circle is

(x^{2}+y^{2}-2x-2y-5)-(x^{2}+y^{2}+4x+6y-19)=0\,

-6x-8y+14=0,3x+4y-7=0\,

Solving these two equations,

-y+1=0,y=1\,

3x+4(1)-7=0,x=1\,

Therefore,the radical centre is (1,1).


Main Page:Geometry:Circles