Q2(i):

Fill in the blanks : (i) A tangent to a circle intersects it in __________ point (s).

Given: A circle and a line segment defined as a tangent to that circle.

To Find: The number of points at which a tangent intersects the circle.

Step 1: Defining a Tangent
By definition, a tangent to a circle is a line that touches the circle at exactly one point. This point is known as the "point of contact" or "point of tangency."

Step 2: Analyzing the Intersection
Let the circle be denoted by $C$ with center $O$ and radius $r$. Let the line be $L$.
If the line $L$ were to intersect the circle at two distinct points, it would be classified as a secant line.
If the line $L$ were to not intersect the circle at all, it would be a non-intersecting line.
Since the line is defined as a tangent, it must satisfy the condition of having exactly one common point with the circumference of the circle.

Step 3: Conclusion
Based on the geometric definition of a tangent in Euclidean geometry, the number of points of intersection is exactly one.

Final Answer: A tangent to a circle intersects it in one point(s).