The Basics of Circles Examples

Suppose the radius of ⊙O is 7 m and OP is 3 m. Is the point P in the exterior of ⊙O, in the interior of ⊙O, or on ⊙O?

First, let's compare the distance from P to O to the radius of ⊙O: OP = 3 m and r, the radius of ⊙O, is 7 m. Since 3 < 7, we know that OP < r. By definition of interior, we know that P is in the interior of ⊙O.

Suppose the radius of ⊙O is 10 km and OP is 10 km. Is the point P in the exterior of ⊙O, in the interior of ⊙O, or on ⊙O?

The distance from O to P in this case is equal to the radius of ⊙O. Therefore, by definition of a circle, P is on ⊙O. It's straddling the fence.

Suppose the radius of ⊙O is 175 cm. OP is 213 cm. Is the point P in the exterior of ⊙O, in the interior of ⊙O, or on ⊙O?

First, let's compare the distance from P to O to the radius of ⊙O: OP = 213 cm and r, the radius of ⊙O, is 175 cm. Since 213 > 175, we know OP > r. By definition of exterior, we know that P is in the exterior of ⊙O.

Suppose a circle is divided into six central angles of the same measure. What is the measure of one of them?

When you're not sure what to do in geometry, the best thing to do is draw a picture.

There are 360° in a full circle. We are given that all 6 of these central angles have the same measure, so all we need to do to find the measure of each one is divide 360° by 6, which equals 60°.