Question

A circle can have _____ parallel tangents at the most.

• A. 2
• B. 1
• C. 0
• D. infinite

Hint:

A circle has infinitely many tangents overall, but for any single direction, only two tangents can remain parallel to each other.

Answer 1

The Correct Option is A

Concept: A tangent to a circle is a straight line that touches the circle at exactly one point. Important properties of tangents:
• A tangent touches the circle at only one point.
• The radius drawn to the point of contact is perpendicular to the tangent.
• From one external point, two tangents can be drawn to a circle.

Step 1: Understand parallel tangents geometrically. Parallel tangents occur on opposite sides of the circle. If one tangent touches the circle from the top side, another parallel tangent can touch it from the bottom side. These two tangents remain parallel because both are perpendicular to the same diameter.

Step 2: Visualize the situation. Suppose a circle has:
• one tangent above the circle,
• another tangent below the circle. These two tangents are parallel.

Step 3: Understand why more than two are impossible. If we try to draw a third line parallel to the other two:
• either it will cut the circle at two points, becoming a secant,
• or it will not touch the circle at all. Hence it cannot remain a tangent. Therefore only two parallel tangents are possible.

Step 4: Final conclusion. A circle can have at most: \[ \boxed{2} \] parallel tangents. Final Answer: \[ \boxed{2} \]