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find the equation of the circle that tangent four lines

(y=x-1) (y=x+1) (y=-x+1) (y=-x+3)

how i can find the center ? enter image description here

Mohammad Ali
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1 Answers1

1

By a simple graph we can easily see that $C(1,1)$ and $R=\frac{\sqrt2}{2}$

enter image description here

thus the equation of the tangent circle is

$$(x-1)^2+(y-1)^2=\frac12$$

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