(D) The given lines are $L_1: x+y-4=0$,$L_2: x-y+2=0$,and $L_3: y-2=0$. These three lines form a triangle. $A$ circle that touches all three lines is

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(D) The given lines are $L_1: x+y-4=0$,$L_2: x-y+2=0$,and $L_3: y-2=0$. These three lines form a triangle. $A$ circle that touches all three lines is an incircle or an excircle of the triangle formed by these lines. For any triangle,there is one incircle and three excircles. Therefore,there are $1+3=4$ circles that touch all three given lines.

Class 11 Mathematics 10-1.Circle and System of Circles Geometrical problems regarding circle and its properties

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The number of circles that touch all the straight lines $x+y=4$,$x-y=-2$,and $y=2$ is

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A
$1$
B
$2$
C
$3$
D
$4$

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10-1.Circle and System of Circles

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Geometrical problems regarding circle and its properties

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The number of circles that touch all the straight lines $x+y=4$,$x-y=-2$,and $y=2$ is

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