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CCGPS Geometry UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MMC9-12.G.C.1-5,G.GMD.1-3 Today’s Question: How do we use angle measures to find measures of arcs? Standard: MMC9-12.G.C.2 AGENDA 1. Notes on Circles 2. Notes on Central Angles 3. Homework Worksheet C Parts of a Circle Circle – set of all points _________ equidistant from a given point called the _____ center of the circle. Symbol: C CHORD: A segment whose endpoints are on the circle Radius RADIUS: P Distance from the center to point on circle Diameter P DIAMETER: Distance across the circle through its center Also known as the longest chord. D = ? r = ? r = ? D = ? Use P to determine whether each statement is true or false. Q 1. RT is a diameter.False R 2. PS is a radius. True P 3. QT is a chord. True 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 a radius Point of Tangency: The point where the tangent intersects the circle Name the term that best describes the notation. Central Angle : An Angle whose vertex is at the center of the circle A Major Arc Minor Arc More than 180° Less than 180° P ACB To name: use 3 letters AB C B APB is a Central Angle To name: use 2 letters Semicircle: An Arc that equals 180° E D To name: use 3 letters EDF P F THINGS TO KNOW AND REMEMBER ALWAYS A circle has 360 degrees A semicircle has 180 degrees Vertical Angles are Equal measure of an arc = measure of central angle A E Q m AB = 96° m ACB = 264° 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. 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 45 A 45 D 110 Arc length is proportional to “r” Classwork • Practice Worksheet Homework: • Practice Worksheet