- Topics At a Glance
**The Basics of Circles**- Center and Radius
- Central Angles
- Arcs
- Arc Measure vs. Length
- Arc Length and Circumference
- Angles and Arcs
- Chords
- Angles and Chords
- Arcs and Chords
- Inscribed Angles
- Inscribed Angle Theorem
- Tangents and Secants
- Perpendicular Tangent Theorem
- Tangents and Multiple Circles
- Circles on the Coordinate Plane
- Equations of Circles
- Circles and Lines

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 ⊙ |

Example 2

Suppose the radius of ⊙ |

Example 3

Suppose the radius of ⊙ |

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*. m∠*BOC* = 50°, m∠*COD* = 140°, 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?