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Learning Target: I can review properties of angles and segments in circles to determine their measure and length. Circles Review: Properties, Angles and Segments Review Agenda: 1. Do Now 2. Embedded Assessment Self-Assess 3. Circles Properties Review 4. Independent Practice 5. Debrief/Note Sheet Creation DO NOW 3/27: Find the radius BO if AB = 4in and AO = 5 in. Embedded Assessment: Vertigo Round Definitions: Radii, Chords, and Tangents A radius is a line segment with one endpoint at the center of the circle and the other endpoint on the circle. A chord is a line segment with both endpoints on the circle A tangent is a line that touches the circle at one point N (the “point of tangency”) D R T O C Property 1: Radius and Tangent When a radius and tangent meet, it forms a 90˚ angle. N R T O Property 2: Radius and Chords A radius that is perpendicular to a chord bisects that chord. R x x C O D Two Chords… Two congruent chords are always the same distance from the center. D R x x C O H Property 3: Two Tangents… Two tangents starting from the same point outside a circle are congruent to the point of tangency. T x x N A O Circles Review: Arcs, Central and Inscribed Angles Review Definition: Arcs An arc is the section of the circumference of a circle between two points. C A O Definition: Central and Inscribed Angles A central angle is an angle with its vertex at the center of the circle (sides are radii) An inscribed angle is an angle with its C T vertex on the circle (sides are chords) O N S I Properties: Arcs, Central and Inscribed Angles The measure of a central angle is the same as the arc it intercepts. The measure of an inscribed angle is ½ of the arc it intercepts. 75˚ C T 75˚ O 20˚ S I 40˚ Circles Review: Angles Formed by Chords, Tangents and Secants Review Equation 1: Angles Formed by Chords The angle formed by 2 chords is ½ of the sum of the two arcs. x = ½(a+b) P L O x b M a x Q Equation 2a: Angles Formed by Secants Secant – a line that intersects the circle at 2 points The angle formed by 2 secants is ½ the difference of the two arcs. x = ½(a-b) P M L x a O b N Q Equation 2b: Angles Formed by Tangent and Secant The angle formed by a tangent and secant is ½ the difference of the two arcs. x = ½(a-b) P A x b a O Q R Equation 3: Angles Formed by Tangents The angle formed by two tangents is the major arc minus 180. x = a – 180 P L O x Q a Learning Target: I can review how to solve problems involving segments in circles, arc length, sector area and equations of a circle. Circles Review: Segment Lengths in Circles Review Agenda: 1. Do Now 2. Circles Properties Review 3. Jeopardy Review Game 4. Embedded Assessment Debrief /Note Sheet Creation DO NOW 3/30: Solve for x. Chord Segment Length When two chords intersect, the products of the two segments lengths of each chord are equal. LA•AQ = MA•AP P L A M Q Secants Segment Length The product of the whole secant segment and the external secant segment of each secant are equal. P LP•LM = LQ•LN M O L N Q Remember! Whole secant • external secant Tangent and Secant Segment Lengths The product of the whole secant segment and the external secant is equal to the tangent segment squared. AR•AQ = AP2 P O A Q R Learning Target: I can review and practice arc lengths, sector area and equations of circles to prepare for the unit exam. Act. 4.5: Area, Circumference, Sectors and Arc Lengths Review Circumference and Area The circumference of a circle is the distance around the outside of the circle. C = 2πr The area is the space the circle covers A = πr2 O Sector and arc length Arc˚/360˚ = fraction of a circle A sector is a fraction of the area Sector area = (arc˚/360 ˚)(πr2) The arc length is a fraction of the circumference Arc length = (arc˚/360 ˚)(2πr) O Act. 4.6: Equation of a Circle Review Equation of a Circle The equation of a circle is made up of 3 parts: The radius (r) The center point (h,k) Another point on the circle (x,y) r2 = (x-h)2 + (y-k)2 (h,k) r (x,y)