Warm-Up The measurements of two vertical angles are 15x and 10x+15. What is the measurement of each angle?

Day 24 Circles: Vocab & Central Angles Today’s Question: How do we use angle measures to find measures of arcs? (MMC9-12.G.C.2)

AGENDA Notes on Circles Notes on Central Angles Practice Worksheet Homework Worksheet

Unit 3 Circles

Circle The set of all points that are __________ from a reference point, the ________. The set of points from a 2-dimensional curve that measures ___. equidistant center C 360 Symbol: C

CHORD: A __________whose __________ lie on the circumference of the circle. segment endpoints

Diameter Also known as the longest chord. P A straight line passing through the _______ of a circle connecting two points on the circle; equal to ______ the radius. center twice P Also known as the longest chord.

Radius The distance from the ______ to a ______ on the circle; equal to ____ the diameter. center P point half

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: A line that intersects a circle at exactly _____ points. TWO

Tangent Line: a LINE that intersects a circle at exactly ____ point and is ____________ to the radius of the circle. ONE PERPENDICULAR Forms a 90°angle with a radius Point of Tangency: The point where the tangent intersects the circle

Point of Tangency TOUCHES Where the tangent line ___________ the circle. TOUCHES

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

Semicircle: An ____ that is ____ of a circle. arc half To name: use 3 letters E D EDF P F Measures EXACTLY 180°.

ACB AB Major Arc Minor Arc More than 180° Less than 180° P AB To name: use 3 letters C To name: use 2 letters B Part of a circle’s circumference that is ____ than its semicircle. Part of a circle’s circumference that is ________ than its semicircle. LESS GREATER

Central Angle : An Angle with its ______ at the _____ of the circle vertex center A P C B APB is a Central Angle

measure of an arc = measure of central angle 96 Q m AB = 96° B C m ACB = 264° m AE = 84° Example 1

A semicircle has 180 degrees Vertical Angles are Equal Always Remember A circle has 360 degrees A semicircle has 180 degrees Vertical Angles are Equal Linear Pairs total 180°.

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

Tell me the measure of the following arcs. m DAB = 240 D A 140 260 m BCA = R 40 100 80 C B Example 2

CONGRUENT ARCS Two arcs that have the same ______ measurement and are either of the same circle or two congruent circles. angle C B D 45 45 110 A Arc length is proportional to “r”