Consider the following statements
I. The perpendicular bisector of a chord of a circle does not pass through the centre of the circle.
II. The angle in a semicircle is a right angle.
Which of the statements given above 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 provided regarding the properties of circles.

### Step 1: Analyze Statement I
**Statement I:** The perpendicular bisector of a chord of a circle does not pass through the center of the circle.

- **Explanation:**
- A chord is a line segment whose endpoints lie on the circle.
- The perpendicular bisector of a chord is a line that divides the chord into two equal parts at a right angle (90 degrees).
- A fundamental property of circles states that the perpendicular bisector of any chord does indeed pass through the center of the circle. Therefore, this statement is **false**.

### Step 2: Analyze Statement II
**Statement II:** The angle in a semicircle is a right angle.

- **Explanation:**
- A semicircle is formed when a diameter divides the circle into two equal halves.
- According to the inscribed angle theorem, any angle inscribed in a semicircle is a right angle (90 degrees).
- Thus, this statement is **true**.

### Conclusion
- **Statement I** is false.
- **Statement II** is true.
- Therefore, only Statement II is correct.

### Final Answer
The correct answer is that **only Statement II is correct**.

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