The number of circles that touch all the thre | vedclass

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(C) The given lines are $L_1: x+y-1=0$,$L_2: x-y-1=0$,and $L_3: y+1=0$.These three lines are not concurrent and form a triangle.For any triangle,there

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$4$

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(C) The given lines are $L_1: x+y-1=0$,$L_2: x-y-1=0$,and $L_3: y+1=0$.These three lines are not concurrent and form a triangle.For any triangle,there exists exactly one incircle that touches all three sides internally.Additionally,there are three excircles,each of which touches one side externally and the extensions of the other two sides.Therefore,the total number of circles that touch all three lines is $1 + 3 = 4$.

The number of circles that touch all the three lines $x+y-1=0$,$x-y-1=0$,and $y+1=0$ is

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