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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

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AGENDA 1.Notes on Circles 2.Notes on Central Angles 3.Homework Worksheet

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

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CHORD: A segment whose endpoints are on the circle

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P RADIUS: Distance from the center to point on circle Radius

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

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D = ? r = ? D = ?

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

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Secant Line: intersects the circle at exactly TWO points

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

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

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P A B C Central Angle : An Angle whose vertex is at the center of the circle Minor ArcMajor Arc Less than 180° More than 180° AB ACB To name: use 2 letters To name: use 3 letters APB is a Central Angle

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

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THINGS TO KNOW AND REMEMBER ALWAYS A circle has 360 degrees A semicircle has 180 degrees Vertical Angles are Equal

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measure of an arc = measure of central angle A B C Q 96 m AB m ACB m AE E = = = 96° 264° 84°

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

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

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

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Classwork Practice Worksheet

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Homework: Practice Worksheet

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