Draw a circle, then identify its interior and exterior.
Always
Practice makes perfect
We are asked to decide if the distance from the center of a circle to a point in the interior of a circle is sometimes, always, or never less than the radius of the circle. Let's begin by drawing a circle with radius r. We need to identify its interior and exterior.
The interior is all points that lie within the circle. The exterior are all other points. We can include this fact in our graph.
By definition, every point that is at a distance of r from the center lies on the circle. Thus, if a point lies in the interior of the circle, its distance to the center will be less than the radius.
We can now write our answer.
The distance from the center of a circle to a point in the interior of the circle is always less than the radius of the circle.
