Which of the following statements is false?

Options

A. Two diameters of a circle will necessarily intersect.
B. The diameter of a circle is always in its interior.
C. Every diameter of a circle is also a chord.
D. Every chord of a circle is also a diameter.

Answer

To determine which of the statements about circles is false, let's analyze each statement step by step.

1. **Statement 1**: Two diameters of circles necessarily intersect.
- **Explanation**: A diameter is a line segment that passes through the center of the circle and has its endpoints on the circle. If we have two diameters, they will intersect at the center of the circle.
- **Conclusion**: This statement is **true**.

2. **Statement 2**: The diameter of a circle is always in its interior.
- **Explanation**: The diameter is a line segment that lies entirely within the circle, connecting two points on the circle's boundary and passing through the center. It cannot exist outside the circle.
- **Conclusion**: This statement is **true**.

3. **Statement 3**: Every diameter of a circle is also a chord.
- **Explanation**: A chord is any line segment that connects two points on the circumference of the circle. Since a diameter connects two points on the circle and passes through the center, it is indeed a special type of chord.
- **Conclusion**: This statement is **true**.

4. **Statement 4**: Every chord of a circle is also a diameter.
- **Explanation**: A chord can be any line segment connecting two points on the circle, but it does not have to pass through the center. Only those chords that pass through the center are considered diameters. Therefore, not every chord is a diameter.
- **Conclusion**: This statement is **false**.

Based on the analysis above, the false statement is **Statement 4**: "Every chord of a circle is also a diameter."