Suppose there exist exactly $n$ circles with non-zero radius in the plane tangent to all the three lines,then the possible values of $n$ is/are

Question

Three distinct lines are drawn in a plane.Suppose there exist exactly $n$ circles with non-zero radius in the plane tangent to all the three lines,then the possible values of $n$ is/are
$(A)0\hspace{1cm}(B)1\hspace{1cm}(C)2\hspace{1cm}(D)4$

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This is multiple correct answer type question.I could imagine only one case when the three lines are making a triangle and a circle is inscribed in that triangle,touching the three lines tangentially.So i guessed answer is $(B)$,but the book says answer is $(A),(C),(D)$.I am confused how is it so?Please help me.

Answer 1

The three cases are A, C and D because as you see in the pictures below. Case B is incorrect because as you said above, having three intersecting lines will generate one circle inbetween, but also three circles are left as you can see in case of 4 circles.