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Entry Task

Entry Task. Circles and Arcs 10-6. Learning Target: I can…. Vocabulary. Circle Center of a circle Diameter Radius Congruent circles Central Angle Semicircle Minor Arc Major arc Arc length. T. Circle – Set of all points equidistant from a given point Center. C.

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Entry Task

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  1. Entry Task

  2. Circles and Arcs10-6 Learning Target: I can…..

  3. Vocabulary • Circle • Center of a circle • Diameter • Radius • Congruent circles • Central Angle • Semicircle • Minor Arc • Major arc • Arc length

  4. T Circle – Set of all points equidistant from a given point Center C ** Name the circle by its center. C D R Radius – Is a segment that has one endpt @ the center and the other endpt on the circle. Ex. CD Diameter – A segment that contains the center of a circle & has both endpoints on the circle. Ex. TR Central Angle – Is an angle whose vertex is the center of the circle. Ex. TCD

  5. Finding measures of Central s B mBAE = 40% of 360 mBAE = (.40) • 360 mBAE= 144 mCAD= 8% of 360 (.08)(360) = 28.8 mDAE = 27% of 360 = 97.2 25% 40% A C 8% 27% D E

  6. More Circle terms Arc – Part of a Circle. * Measured in degrees Minor Arc – Smaller than a semicircle. (< 180°) * Named by 2 letters * Arc Measure = measure of central  * Ex: Major Arc – Greater than a semicircle. (> 180°) * Name by 3 letters * Order matters * Ex: * Measure = Central  R S P T Semicircle – Half of a Circle. * Name by 3 letters * Ex:

  7. Arcs Continued Adjacent Arcs – Are arcs of the same circle that share a common endpoint. Ex: and B C A Arc Addition!! m= m+ m

  8. Ex 1 : Finding the measures of Arcs C 32° B 32 m= m = m= m= mBOC = m+ m m– m m– m 58 32 D O = 32 + 58 = 90 148° 122° = 180 – 58 = 122 A = 180 – 32 = 148

  9. Circumference • Circumference–the distance around the circle. C = d C = 2r or Pi 3.14 Radius of Cirlce Diameter of circle

  10. Ex. 2: Find the circumference of the following circle. C = 2r =2(9cm) =18 cm = 56.5cm 9cm

  11. 16.1 16.1 11.4 16.1 32.2 22.8 11.4 32.2 22.8 9.4 29.53 A tire on the outside travels about 29.53 ft farther than a tire on the inside.

  12. 50 310 50 140 x+y

  13. Arc PR = • Arc RS = • Arc PRQ = • Arc PQR = 77 103 208 283

  14. Arc Length • The measure of an arc is in degrees. • Arc Length – Is a fraction of a circle’s Circumference. • It is the length of a piece of string that would wrap around that part of the circle. A C B

  15. m 2r Length of = 360 Measure of the arc. It is in Degrees. The Circumference Ex: An arc of 40 represents 40/360 or 1/9 of the circle. We call this the “circle fraction” as it represents the portion of the circle in question.

  16. Find the length of in M. m= 210 B Length of = m/360 • 2r 18cm 150 M C = 2r = 2(18cm) = 113cm A Length of = (210/360) • (113cm) = 66cm D

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