Which statement about a circle is true?

Which statement about a circle is true?

• A. It has four sides
• B. Its center is always outside the circle
• C. The distance from the center to any point on the circle is the radius
• D. The diameter is a line segment outside the circle

Answer: (C)

The key idea here is the distance from the center to points on the circle, which defines the radius. By definition, a circle is the set of all points at a fixed distance from a center, and that fixed distance is the radius. So the distance from the center to any point on the circle is precisely the radius. The other statements don’t fit: a circle has no sides, it’s a continuous curved boundary; the center is inside the circle, not outside; and a diameter is a line segment that lies entirely inside the circle, with endpoints on the circle and passing through the center, not outside it.

The key idea here is the distance from the center to points on the circle, which defines the radius. By definition, a circle is the set of all points at a fixed distance from a center, and that fixed distance is the radius. So the distance from the center to any point on the circle is precisely the radius.

The other statements don’t fit: a circle has no sides, it’s a continuous curved boundary; the center is inside the circle, not outside; and a diameter is a line segment that lies entirely inside the circle, with endpoints on the circle and passing through the center, not outside it.