Question

A circle may have ______ parallel tangents.

Answer 1

A circle may have infinitely many parallel tangents.

Explanation:

For any given direction there can be one tangent on each side of the circle — their perpendicular distances from the centre are +r and −r, so only two parallel lines can be tangent to the circle. Also, tangents at the endpoints of a diameter are parallel, which shows such a pair exists.