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 ofthe 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 thecenter. R D x x O H C Property 3: Two Tangents
Two tangents starting from the same point outside a circleare 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 betweentwo points. C A O Definition: Central and Inscribed Angles
A central angle is an angle with its vertex at the center of thecircle (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 itintercepts. The measure of an inscribed angle is 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 of the sum of the twoarcs. x = (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 the difference of the twoarcs. x = (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 the difference ofthe two arcs. x = (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 minus180. 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 twosegments lengths of each chord are equal. LAAQ = MAAP P L A M Q Secants Segment Length
The product of the whole secant segment and the external secantsegment of each secant are equal. LPLM = LQLN Remember! Whole secant external secant P M O L N Q Tangent and Secant Segment Lengths
The product of the whole secant segmentand the externalsecant is equal to the tangent segment squared. ARAQ = 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 theoutside of the circle. C = 2r The area is the space the circle covers A = r2 O Sector and arc length Arc/360 = fraction of a circle
A sector is a fraction of the area Sector area = (arc/360 )(r2) The arc length is a fraction of the circumference Arc length = (arc/360 )(2r) 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)