# At a Glance - The Basics of Circles

Mathematicians like to define things before they start talking about them. This is a good idea in other areas of life too. Ever brought a cake pan to a baseball game because you heard there would be a batter?

Given a point O and a distance r, the circle with center O and radius r is the set of all points in a plane that are exactly r units away from O. Easy enough, right?

#### Example 1

 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?

#### Example 2

 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?

#### Example 3

 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?

#### Example 4

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

#### Exercise 1

Consider a circle with center O and radius 20 m. Is P such that OP = 8 m in the interior of the circle, in the exterior of the circle, or on the circle?

#### Exercise 2

Consider a circle with center O and radius 20 m. Is Q such that OQ = 30 cm in the interior of the circle, in the exterior of the circle, or on the circle?

#### Exercise 3

Consider a circle with center O and radius 20 m. Is S such that OS = 20 m in the interior of the circle, in the exterior of the circle, or on the circle?

#### Exercise 4

Consider a circle with center O and radius 20 m. Is O in the interior of the circle, in the exterior of the circle, or on the circle?

#### Exercise 5

Consider a circle with center O and radius 20 m. Is T such that OT = 100 m in the interior of the circle, in the exterior of the circle, or on the circle?

#### Exercise 6

Consider a circle with center O and radius 20 m. Is U such that OU > OS in the interior of the circle, in the exterior of the circle, or on the circle?

#### Exercise 7

Consider a circle with center O and radius 20 m. Is V such that OS < OV < OU in the interior of the circle, in the exterior of the circle, or on the circle?

#### Exercise 8

In the figure below, points A, B, C, and D are on ⊙O. If m∠BOC = 50°, m∠COD = 140°, and m∠DOA = 65°, what is m∠AOB?

#### Exercise 9

In the figure below, suppose now that m∠BOC = 67° instead of 50°. How does the measure of m∠AOB change?