Which statements are true? Select all that apply.

Question

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.