Sec. 10 – 2 Circles and Arcs Objectives: 1) To find the measures of central angles and arcs. 2) To find circumferences and arc lengths.

T C R D Circle – Set of all points equidistant from a given point Center ** Name the circle by its center. Radius – Is a segment that has one the center and the other endpt on the circle. Ex. CD Diameter – A segment that contains the center of a circle & has both endpts on the circle.Ex. TR Central Angle – Is an  whose vertex is the center of the circle.Ex.  TCD C ** 360°

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

More Circle terms P S R T 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: RS Major Arc – Greater than a semicircle. (> 180°) * Name by 3 letters * Order matters * Ex: RTS * Measure = Central  Semicircle – Half of a Circle. * Name by 3 letters * Ex: TRS = 180 

Arcs Continued A B C Adjacent Arcs – Are arcs of the same circle that have exactly one point in common. Ex: AB and BC mBCA = mBC + mCA Arc Addition!!

Ex 1 : Finding the measures of Arcs O B C D A 58  32  mBC = mDB = mAD = mAB = m  BOC = mBC + mCD mADC – mCD mABC – mBC 32 = = 90 = 180 – 58 = 122 = 180 – 32 = ° 122° 148°

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

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

Example 2: Circumference The diameter of a bicycle wheel is 22in. To the nearest whole number, how many revolutions does the wheel make when the bicycle travels 100ft? Step 1: Convert diameter to feet. 12in in a foot C =  d =(1.83ft)  = 5.8ft Step 2 finish the prob 100ft/5.8ft = = 17.2 turns 22/12 = 1.83ft

Back to Arcs!! The measure of an arc is in degrees. Arc Length – Is a fraction of a circle’s Circumference. –It is the piece of string that would form the part of the circle. A B C

Length of AB = mAB 360 2r2r Measure of the arc. It is in Degrees. The Circumference Ex: An arc of 40  represents 40/360 or 1/9 of the circle. * Which means 1/9 of the Circumfernece.

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