Arcs and Chords Chapter 10 2 Recognize major

Arcs and Chords Chapter 10 -2

• Recognize major arcs, minor arcs, semicircles, and central angles and their measures. • Find arc length. • central angle • arc • minor arc • major arc • semicircle Standard 7. 0 Students prove and use theorems involving the properties of parallel lines cut by a transversal, the properties of quadrilaterals, and the properties of circles. (Key)

Central Angle • An angle whose vertex is the center of the circle • The sum of the central angles of a circle = 360 o – As long as they don’t B C overlap Central Angle A BCA is a Central Angle

A. 9 B. 21 C. 65 D. 30 A. B. C. D. A B C D

A. 15 B. 25 C. 40 D. 75 A. B. C. D. A B C D

Arcs Def: A portion of a circle cut by two radii • Minor Arc—an arc formed by the interior of two radii with a central angle less than 180 o • Major Arc—an arc formed by the exterior of two radii with a central angle less than 180 o • Semi-Circle—an arc formed by the endpoints of a diameter • The measure of an arc is equal to the measure of the Animation: Arcs central angle that forms it of a Circle • Two arcs are if and only if their corresponding central angles are . (in the same circle or circles)

m AB = 60 ° m ADB = 300 ° D B 60° Minor Arc A P Major Arc

Find the arc measures m AB = 80 ° m DE = 45 ° m AF = 45 ° 55 ° m DF = 180 ° m BF = 125 ° 45 ° m BD = 55 ° m DFB = 305 ° m FE = 135 °

Arc Addition • The measure of an arc formed by two adjacent arcs is the sum of the measures of the 2 arcs m CA + m DC = 72 ° A m CA = 40 ° B C m DC = 32 ° D m DA = 72 °

Arc Addition Sample Problem • Find m ABD m CA + m DC = m AD = m ABD 4 x + 7 + 2 x + 5 = 8 x 6 x + 12 = 8 x A m AC = 4 x + 7 ° B 8 x ° C m CD = 2 x + 5 ° D 12 = 2 x 6=x m ABD = 8(6) m ABD = 48 °

Measures of Arcs 46 o

Measures of Arcs is a minor arc, so is a semicircle. 46 o Answer: 90

Measures of Arcs 46 o Answer: 67

Measures of Arcs 46 o 44 o 46 o Answer: 316

A. 54 B. 27 C. 108 D. 72 1. 2. 3. 4. A B C D

A. 54 B. 126 C. 108 D. 72 1. 2. 3. 4. A B C D

A. 126 B. 234 C. 180 D. 288 1. 2. 3. 4. A B C D

Circle Graphs A. BICYCLES This graph shows the percent of each type of bicycle sold in the United States in 2001. Find the measurement of the central angle representing each category.

Circle Graphs B. BICYCLES This graph shows the percent of each type of bicycle sold in the United States in 2001. Is the arc for the wedge named Youth congruent to the arc for the combined wedges named Other and Comfort? Answer: no

Arc Length • Arc length is a part of the circumference of a circle. OR

Find the Arc Length of AB m. AB = 60 o A r = 12 cm B

Arc Length In and. Write a proportion to compare each part to its whole.

Arc Length degree measure of arc degree measure of whole circle arc length circumference Now solve the proportion for. Multiply each side by 9. Simplify. Answer: The length of is π units or about 3. 14 units.

A. 7. 88 B. 15. 75 C. 49. 48 D. 24. 74 A. B. C. D. A B C D

Homework Chapter 10. 2 • Pg 567 11 - 28, 33 - 35 all