Suppose a circle and a line intersect in a plane. what is the smallest number of points at which they can touch?

The smallest number of points at which they can touch is:

                                  1

Tangent of a circle--

The tangent to a circle is a straight line that touches the curve at just one point i.e. it " just crosses " the curve.

Hence, here it is given that a circle and a line intersect in the curve.

i.e. the line meets the circle at at least one point.

As the minimum number of intersection point is 1 (i.e. a tangent to the circle )

Hence, the answer is:

      1