Question

Which statements are true? Select all that apply.

Question 2 options:

The radius is twice the diameter of a circle.


Central angles have the vertex on the center of the circle.


The arc length in degrees is the same as the central angle.


The diameter is a chord.


Inscribed angles have the vertex on the center of the circle.

Answer 1

Let's evaluate each statement one by one to determine which are true:

1. **The radius is twice the diameter of a circle.**
**False.** The radius is half the diameter of a circle.

2. **Central angles have the vertex on the center of the circle.**
**True.** A central angle is defined as having its vertex at the center of the circle.

3. **The arc length in degrees is the same as the central angle.**
**True.** The measure of an arc in degrees is equal to the measure of the central angle that intercepts it.

4. **The diameter is a chord.**
**True.** The diameter of a circle is indeed the longest chord and qualifies as a chord, which is a segment whose endpoints lie on the circle.

5. **Inscribed angles have the vertex on the center of the circle.**
**False.** An inscribed angle has its vertex on the circumference of the circle, not at the center.

Based on the evaluations, the true statements are:
- Central angles have the vertex on the center of the circle.
- The arc length in degrees is the same as the central angle.
- The diameter is a chord.