Question

Lines $l$ and $m$ and two circles lie in a plane. If $l$ passes through the centers of the two circles and if $m$ is parallel to $l$, which of the following could NOT be the number of points at which $m$ intersects the circles?

• A. $0$
• B. $1$
• C. $3$
• D. $4$
• E. $5$

Answer 1

The correct option is E $5$

Line $l$ is passing through the center of $2$ circles. And line $m$ is parallel to $l$.

Now if the line $m$ is moved along the plane as shown in the figure.

We can see that the line $m$ touch circles once, twice, thrice and four times. Or never touches at all.

Hence Option E.