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Name: ____________________________ Review Part 1 Geometry Pd. __________ Date: _____ CENTRAL ANGLES NSCRIBED ANGLES VERTEX MUST BE ON THE CENTER OF THE CIRCLE. VERTEX MUST BE ON THE CIRCLE. RULE: ANGLE =HALF THE INTERCEPTED ARC 13-1 RULE: ANGLE INTERCEPTED 13-2 Thales Theorem ANGLES FORMED BY 2 CHORDS Cyclic Quadrilaterals βBOW βTIE ANGLESβ VERTEX is NOT on the center and NOT on the circle. Quadrilateral inscribed in a circle RULE: 13-3 = ARC π¨πΉπͺ #π+π¨πΉπͺ #π π OPPOSITE ANGLES ARE SUPPLEMETARY (ADD UP tO 180 ) Watch out! This is not necessarily a parallelogram, so consecutive angles are not supplementary. ONLY OPPOSITE ANGLES. SPECIAL INSCRIBED ANGLES Sneaky Angle Formed by a Tangent and chord Rule: ANGLE =HALF THE INTERCEPTED ARC SPECIAL CASE Formed by a secant and chord Rule: Find the measure of inscribed adjacent angle and subtract from 180. If the chord is a diameter, rt angles! 13-4 ANGLES FORMED BY TWO SECANTS, OR TWO TANGENTS OR A SECANT AND A RULE: Outside β‘ = Special Case- β Ice cream TANGENT. Coneβ Narc + Outside angle = 180 ππ¨πΉπͺβπ΅π¨πΉπͺ π 1) Always solve for arcs first. (HIGLIGHT DIAMETERS!).KNOW HOW TO WORK WITH RATIOS! BIG CIRCLES 2) Solve the parts in the order they are presented in for the problem. 3) GO SLOW. 4) Highlight parts you're solving for (in different colors). 5) Fill in/mark up the diagram. Station 1: Arcs and Angles 1) In the accompanying diagram of circle O, What is the measure of and . ? 1) 1040 2) 800 3) 520 4) 400 2) In the accompanying diagram of circle O, chord Μ = 80. mπ΄π· What is ? is parallel to diameter , is drawn, and 1) 90 2) 40 3) 130 4) 100 3) In the accompanying diagram of circle O, chords What is ? 4) In the diagram below, is tangent to circle O, and and intersect at E and is a chord. If . , find the measure of . 5) Tangents and are drawn from point times the minor arc. Find . 6) In the accompanying diagram, to the same circle. The major arc intercepted by the tangents is three is tangent to circle O at Q and is a secant. If and , find . 7) In the accompanying diagram of circle O, , is a diameter, and radius is drawn. If , find . 8) A quadrilateral is CYCLIC if their __________________________ angles are _______________ Using your answer in #8, answer the following: 8) . 9) Station 2: Big Circle Problems 1) 2) Push yourself! 3) In the diagram, PA is tangent to circle O at A, PBC is a secant, and AB and CA are chords. If m<P = 40 o and Μ : ππ΄π΅ Μ = 7: 3, findβ¦ ππ΄πΆ Μ a) ππ΄πΆ Μ b) ππ΅πΆ c) π < π΄πΆπ΅ HINT ππππβππππ Start with 2 d) π < π΄π΅πΆ f) π < πΆπ΄π΅ g) π < π΄π΅π