Consider the following statements
I. The tangent of a circle is a line that meets the circle in one and only one point.
II. The tangent of a circle at the end point of the diameter is perpendicular to the diameter.
Which of the above statements is/are correct?

Options

A. Only I
B. Only II
C. Both I and II
D. Neither I nor II

Answer

To solve the problem, we need to analyze the two statements regarding the tangent of a circle.

**Step 1: Analyze Statement I**
- Statement I states: "The tangent of a circle is a line that meets the circle in one and only one point."
- By definition, a tangent to a circle is indeed a line that touches the circle at exactly one point. This is a fundamental property of tangents. Therefore, Statement I is **correct**.

**Step 2: Analyze Statement II**
- Statement II states: "The tangent of a circle at the end point of the diameter is perpendicular to the diameter."
- To understand this, consider a circle with a diameter. If we take one endpoint of the diameter and draw a tangent line at that point, the tangent line will be perpendicular to the radius of the circle at that point. Since the radius at the endpoint of the diameter is also part of the diameter, the tangent will indeed be perpendicular to the diameter at that endpoint. Thus, Statement II is also **correct**.

**Conclusion:**
Both statements I and II are correct.

**Final Answer:**
Both statements are correct.

---