Question

What will be the correct option for the following statement? How many parallel tangents a circle can have at most?
A. 1
B. 2
C. Infinite
D. None of these

Answer 1

Hint: As we know that two lines are parallel if any only if they do not intersect or touch each other. Tangent is a line drawn to the circle that touches the circle at only one point.

Complete step-by-step answer:
There can be infinite tangents possible because there are infinite points in a circle.
But here we are asked to find parallel tangents and we know that two lines are parallel if and only if they never touch each other.
So, this is only possible in a circle if tangents are drawn from the two ends of a diameter.

So, at most a circle can only have two parallel tangents which touch the circle at the end of its diameter.
Now there can be infinite such pairs of parallel tangents because there can be an infinite number of diameters that can be formed in a circle. But each pair can have only two tangents.
Hence, the correct option will be B.

Note: Whenever we come up with this type of problem then first, we have to only use definition of parallel lines and definition of tangent to circle. In this type of question, no calculation is needed.