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## Brain Buster

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**Brain Buster**1. Draw a circle with r = 4 and center A. 2. What is the diameter of the circle? 3. Explain the difference between a secant & a chord 4. What do you know about a tangent line and the radius drawn to the point of tangency?**Math II**UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MM2G1, MM2G2 Today’s Question: How do we use angle measures to find measures of arcs? Standard: MM2G3.a,d**Arcs and**Section 6.2, 6.3 Chords**Central Angle :**An Angle whose vertex is at the center of the circle ACB AB A Major Arc Minor Arc More than 180° Less than 180° P To name: use 3 letters C To name: use 2 letters B APB is a Central Angle**EDF**Semicircle: An Arc that equals 180° To name: use 3 letters E D 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**m AB m ACB m AE A E 96 Q = 96° B C = 264° = 84°**Arc Addition Postulate**m ABC = m AB + m BC A C B**m DAB =**Tell me the measure of the following arcs. 240 D A 140 260 m BCA = R 40 100 80 C B**CONGRUENT ARCS**Congruent Arcs have the same measure and MUST come from the same circle or of congruent circles. C B D 45 45 110 A**In the same circle, or in congruent circles, two minor arcs**are congruent if and only if their corresponding chords are congruent. B C AB CD IFF AB DC A D**Ex. 1**60 120 120 x x = 60**Ex. 2**2x x + 40 2x = x + 40 x = 40**What can you tell me about segment AC if you know it is the**perpendicular bisectors of segments DB? D It’s the DIAMETER!!! A C B**Ex. 3 If a diameter of a circle is perpendicular to a**chord, then the diameter bisects the chord and its arc. x = 24 24 y 60 y = 30 x**Example 4**EX 2: In P, if PM AT, PT = 10, and PM = 8, find AT. P A M MT = 6 T AT = 12**Example 5**In R, XY = 30, RX = 17, and RZ XY. Find RZ. X RZ = 8 R Z Y**Example 6**IN Q, KL LZ. IF CK = 2X + 3 and CZ = 4x, find x. Q x = 1.5 C Z K L**In the same circle or in congruent circles, two chords are**congruent if and only if they are equidistant from the center. B AD BC IFF LP PM A M P L C D**Ex. 7: InA, PR = 2x + 5 and QR = 3x –27.**Find x. R A x = 32 Q P**Ex. 8: IN K, K is the midpoint of RE. If TY = -3x + 56**and US = 4x, find x. U T K E R S x = 8 Y