Question

A circle can have ........ parallel tangents at the most.

Answer 1

Hint: Draw a circle, and draw tangents at the point of contact of diameter to visually determine the no of parallel tangents can be drawn at most.

Complete step-by-step answer:
We know that for each tangent to a circle the radius to the point of contact with the circle is perpendicular to the tangent line.
So, two parallel tangents then basically mean that their contact radii form a perfect diameter of the circle.
This diameter meets the circle in exactly two points. So, there is no more space for a third or more parallel tangents. Hence, A circle can have 2 parallel tangents at the most.

Note: Circle can have at most 2 parallel tangents, one at a point on it and the other at a point diametrically opposite to it. This is a proven mathematical fact and can be seen visually in the above picture.