Test is next class Test is open note Circle review Test is next class Test is open note

Find the area and circumference of the circle below that has a radius of 8.5 cm. 𝐴=𝜋 𝑟 2 𝐴=𝜋∗ 8.5 2 𝐴=72.25𝜋 𝐴≈226.98 𝑐𝑚 2 𝐶=2𝜋𝑟 𝐶=2∗𝜋∗8.5 𝐶=17𝜋 𝐶≈53.41𝑐𝑚 8.5

Inscribed angles 1. 3𝑥−3=120/2 3𝑥−3=60 3𝑥=63 𝑥=21 ∠𝐵=180−50−70 ∠𝐵=60° 1. 3𝑥−3=120/2 3𝑥−3=60 3𝑥=63 𝑥=21 ∠𝐵=180−50−70 ∠𝐵=60° Arc AC=60*2 Arc AC=120° Arc CBA =360°−120° Arc CBA =240°

Circle vocabulary Minor arc Central angle radius Inscribed angle Tangent line diameter chord semicircle Major arc

More inscribed angles 𝑥= 58+106 /2 𝑥=82° 𝑦=(360−58−106)/2 𝑦=98° 𝑧=180−93 𝑧=87°

Length of intersecting chords 3𝑥=6∗4 3𝑥=24 𝑥=8

Area of a segment Segment = sector –triangle sector: 𝐴= 120 360 ∗𝜋 ∗24 2 𝐴= 1 3 ∗𝜋 ∗24 2 𝐴=192𝜋≈603.19 Triangle: 𝐴=.5∗𝑠𝑖𝑑𝑒∗𝑠𝑖𝑑𝑒∗sin⁡(𝑖𝑛𝑐𝑙𝑢𝑑𝑒𝑑 𝑎𝑛𝑔𝑙𝑒) 𝐴=.5∗24∗24∗sin⁡(120°) 𝐴≈249.42 Segment: 𝐴=603.1∗−249.42=353.47 𝑢𝑛 2

Length of a chord Step 1: connect end points of chord to center of circle to make a triangle Step 2: WZ=XZ=20/2=10 Step 3: angle Z= 130 Length of chord: choice 1= law of cosines 𝑊𝑋 2 = 10 2 + 10 2 −2∗10∗10∗cos⁡(130°) 𝑊𝑋 2 =328.56 𝑊𝑋=18.13 Choice 2= law of sines: Angle W= (180-130)/2=25 𝑊𝑋 sin⁡(130°) = 10 𝑠𝑖𝑛25° 𝑊𝑋=(10𝑠𝑖𝑛130)/𝑠𝑖𝑛25 WX=18.13 Length of chord WX

Equations and graphing circles Identify the center and radius on the equation below and then graph it on a separate sheet of paper. (𝑥−4) 2 + (𝑦+2) 2 =16 Center= (4, -2) R=4