Which of the following statements is false?

Options

A. Two diameters of a circle will necessarily intersect.
B. The centre 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 following statements is false, let's analyze each statement one by one.

1. **Statement 1:** Two diameters of the circle will necessarily intersect.
- A diameter is a line segment that passes through the center of the circle and has its endpoints on the circle. Since all diameters pass through the center, any two diameters will intersect at the center. Therefore, this statement is **true**.

2. **Statement 2:** The center of the circle is always in the interior.
- The center of the circle is the point that is equidistant from all points on the circle. By definition, this point lies within the circle, making this statement **true**.

3. **Statement 3:** Every diameter of the circle is also a chord.
- A chord is defined as a line segment whose endpoints lie on the circle. Since a diameter has its endpoints on the circle and passes through the center, it meets the criteria of a chord. Thus, this statement is **true**.

4. **Statement 4:** Every chord of a circle is also a diameter.
- This statement is incorrect. While all diameters are chords, not all chords are diameters. A chord can be any line segment connecting two points on the circle, but it does not necessarily have to pass through the center. Therefore, this statement is **false**.

Based on the analysis above, the false statement is:

**Answer:** Every chord of a circle is also a diameter.

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