Circle Vocabulary

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

CHORD: A segment whose endpoints are on the circle

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

RADIUS: Distance from the center to a point on the circle… The radius is half ½ of the diameter P

Radius = ½ diameter or Diameter = 2r Formula Radius = ½ diameter or Diameter = 2r

D = ? 24 32 12 r = ? 16 r = ? 4.5 6 D = ? 12 9

Use P to determine whether each statement is true or false. Q R T S True: thumbs up False: thumbs down

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

Secant Radius Diameter Chord Tangent Name the term that best describes the notation. Secant Radius Diameter Chord Tangent

REVIEW Identify the following parts of the circle. A B E DC AB AC line E chord radius diameter tangent secant Note: The following are possible answers. radius diameter chord midpoint secant tangent

An angle whose vertex is at the center of the circle 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 Minor Arc ACB AB Major Arc More than 180° Less than 180° ACB P AB To name: use 3 letters C To name: use 2 letters B

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

Identify the parts

THINGS TO KNOW AND ALWAYS REMEMBER 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 n° C If ∠ ABC is 80°, what is the measure of arc AC? A x° B ° m AC = 80°

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 major arc = 360° – m xz (minor arc) 68° =360° – 68° m xz (major arc) = 292° 68° y 292° z

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

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

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

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

Textbook p. 396 #11 p. 404 #11 – 16, 25 – 30, 38