Step-by-Step Solution
Key Concept: A tangent to a circle is a straight line that touches the circle at exactly one point. Since every point on the circumference can serve as a point of contact, and there are infinitely many points on the circumference, the circle can have infinitely many distinct tangents.
1. Definition of a tangent: A line is called a tangent to a circle if it meets the circle at exactly one point (the point of contact).\
2. Point of contact: Any point on the circumference of the circle can be chosen as a point of contact.\
3. Number of points on the circumference: The set of points on a circle is infinite (uncountably many).\
4. Correspondence: For each distinct point of contact there exists a unique tangent line (the line perpendicular to the radius drawn to that point).\
5. Conclusion: Hence, as there are infinitely many points on the circle, there are infinitely many distinct tangents that can be drawn to the circle.
Therefore, a circle can have infinitely many tangents.
Correct Answer: Infinitely many (an unlimited number of) tangents.