Circles Review: Properties, Angles and Segments 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 DO NOW 3/27: Find the radius BO if AB = 4in and AO = 5 in. Agenda: Do Now Embedded Assessment Self-Assess Circles Properties Review Independent Practice Debrief/Note Sheet Creation

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 (the “point of tangency”) N 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 D x x O C

Two Chords… Two congruent chords are always the same distance from the center. R D x x O H C

Property 3: Two Tangents… Two tangents starting from the same point outside a circle are congruent to the point of tangency. T x x A N O

Circles Review: Arcs, Central and Inscribed Angles

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 vertex on the circle (sides are chords) C T N O 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 40˚ I

Circles Review: Angles Formed by Chords, Tangents and Secants

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 a L O x x b M 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 O a b L x 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 O a b x A Q R

Equation 3: Angles Formed by Tangents The angle formed by two tangents is the major arc minus 180. x = a – 180 P O a x L Q

Circles Review: Segment Lengths in Circles 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 DO NOW 3/30: Solve for x. Review Agenda: Do Now Circles Properties Review Jeopardy Review Game Embedded Assessment Debrief /Note Sheet Creation

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. LP•LM = LQ•LN Remember! Whole secant • external secant P M O L N Q

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

Act. 4.5: Area, Circumference, Sectors and Arc Lengths 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)