Question

i.The no.of circles touching all the lines $x+y-4=0,x-y+2=0,x+y=3$ is $2$.
ii. The no.of circles touching all the lines $2x+3y-7=0,4x+6y-1=0,x+y+1=0$ is $3$.

Which of above statement is correct?

• A. Only i
• B. Only ii
• C. Both i & ii
• D. Neither i nor ii

Answer 1

The correct option is A Only i

It is clear from the figure that one circle can be drawn to the left of $x+y=-2$ and the other on the right such that they are tangents to all 3 lines. Similar is the case for part ii where we have 2 parallel lines and one intersecting line. Hence, there can be only 2 possible circles satisfying these constraints.