Circle Vocabulary C Circle set of all pointsequidistant

Circle Vocabulary

C Circle – set of all pointsequidistant _____ from a given point called the center _____ of the circle. Symbol: C

CHORD: A segment whose endpoints are on the circle

DIAMETER: P Distance across the circle through its center Also known as the longest chord.

RADIUS: P Distance from the center to point on circle

Formula Radius = ½ diameter or Diameter = 2 r

Use P to determine whether each statement is true or false. Q R P T S

Secant Line: intersects the circle at exactly TWO points

Tangent Line: a LINE that intersects the circle exactly ONE time Forms a 90°angle with one radius Point of Tangency: The point where the tangent intersects the circle

Name the term that best describes the notation. t n a Sec s u i Rad Diame t e r Ch or d t n e g n a T

REVIEW Identify the following parts of the circle. 1. DC • chord 2. AB • radius 3. AC • diameter 4. line E • 5. DC • D A B C E tangent secant Note: The following are possible answers. radius diameter chord midpoint secant tangent

Central Angles An angle whose vertex is at the center of the circle

Central angle A P C B <APB is a Central Angle

3 Types of Arcs A Major Arc Minor Arc More than 180° Less than 180° P ACB To name: use 3 letters C AB B To name: use 2 letters

Semicircle: An Arc that equals 180° D E To name: use 3 letters P F EDF

Identify the parts

THINGS TO KNOW AND REMEMBER ALWAYS A circle has 360 degrees A semicircle has 180 degrees Vertical Angles are CONGRUENT Linear Pairs are SUPPLEMENTARY

Formula measure Arc = measure Central Angle

Measure of Arcs & Angles In a circle, the measure of the central angle is always equal to the measure of its intercepted arc. x=n m ∠ ABC = m AC • If ∠ ABC is 80°, what is the measure of arc AC? m AC = 80° n° A C x° B°

Measure of Arcs & Angles EXAMPLE: In the diagram below, if the m ∠ xyz is 68°, find the measure of a. ) minor arc and b. ) major arc. SOLUTION: a. measure of minor arc m ∠xyz = m xz (since ∠xyz is a central angle) x m xz = 68° b. measure of major arc 68° major arc = 360° – m xz (minor arc) =360° – 68° y m xz (major arc) = 292° 68° z

Find the measures. EB is a diameter. m AB = 96° A E m ACB = 264° Q m AE = 84° 96 B C

Arc Addition Postulate A C B m ABC = m AB + m BC

Tell me the measure of the following arcs. AC is a diameter. m DAB =240 m BCA = 260 D C 140 R 40 100 80 B A

Congruent Arcs have the same measure and MUST come from the same circle or of congruent circles. C B A 45 45 D 110 Arc length is proportional to “r”

INSCRIBED ANGLES An angle whose vertex is on the circle. The measure of an inscribed is ½ the measure of the intercepted arc.