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(B) Let the required circle be $x^2+y^2+2gx+2fy+c=0$. Since it cuts the given circles orthogonally,the condition $2g_1g_2 + 2f_1f_2 = c_1 + c_2$ must

Vedclass · Accepted Answer

$\sqrt{3}$

Vedclass · Answer

(B) Let the required circle be $x^2+y^2+2gx+2fy+c=0$. Since it cuts the given circles orthogonally,the condition $2g_1g_2 + 2f_1f_2 = c_1 + c_2$ must be satisfied for each. For $x^2+y^2-4x-4y+3=0$: $2g(-2) + 2f(-2) = c + 3 \implies -4g - 4f = c + 3$. For $x^2+y^2+4x-4y+3=0$: $2g(2) + 2f(-2) = c + 3 \implies 4g - 4f = c + 3$. For $x^2+y^2+4x+4y+3=0$: $2g(2) + 2f(2) = c + 3 \implies 4g + 4f = c + 3$. Subtracting the first two equations: $8g = 0 \implies g = 0$. Subtracting the last two equations: $8f = 0 \implies f = 0$. Substituting $g=0$ and $f=0$ into any equation: $0 = c + 3 \implies c = -3$. The equation of the circle is $x^2+y^2-3=0$,which is $x^2+y^2=3$. The radius is $\sqrt{r^2} = \sqrt{3}$.

The radius of the circle which cuts all the three circles $x^2+y^2-4x-4y+3=0$,$x^2+y^2+4x-4y+3=0$,and $x^2+y^2+4x+4y+3=0$ orthogonally is

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