UNIT 5 Circles

Key Term (only write what’s in RED) Circle: the set of a all points that are a given distance from a given point called the center KEEP IN MIND: A circle is a shape with all points the same distance from its center. A circle is named by its center. Thus, the circle below is called circle A since its center is at point A. Some real world examples of a circle are a wheel, a dinner plate and (the surface of) a coin. written as: A (circle A)

Key Terms Do you remember…? Arc: part of the circumference of a circle Semicircle: half of a circle (180°) Minor Arc: smaller than a semicircle (2 letters) Major Arc: greater than a semicircle (3 letters)

Identify: Semicircles  ________________________________ Minor Arcs  ________________________________ Major Arcs  ________________________________ B C E BONUS What’s the name of the circle?? A D

*the measure of an arc is EQUAL to the measure of its CENTRAL ANGLE

EX. 1 a) Find the measure of each arc in Q. mCD: 40° mAD: 180° - 40° = 140° mCAD: 360° - 40° = 320° or 140° + 180° = 320° mDCA: 360° - 140° = 220° or 180° + 40° = 220° D 40° A C Q

EX. 1 (YOU TRY) B) Find the measure of each arc in Q. mDC: ___________ mEB: ___________ mDAC: ___________ mACD: ___________ Q C A 35° 75° E D

Parts of a Circle KEEP IN MIND: The distance across a circle through the center is called the diameter. A real-world example of diameter is a 9-inch plate. The radius of a circle is the distance from the center of a circle to any point on the circle. If you place two radii end-to-end in a circle, you would have the same length as one diameter. Thus, the diameter of a circle is twice as long as the radius. A chord (pronounce CORD) is a line segment that joins two points on a curve. In geometry, a chord is often used to describe a line segment joining two endpoints that lie on a circle. The circle to the top right contains chord AB.

CIRCLE FORMULAS C = πd or C = 2πr Why are these equations the same?? CIRCUMFERENCE AREA C = πd or C = 2πr Why are these equations the same?? A = πr×r or A = πr2 Why are these equations the same??

Ex. 2 Find the circumference and area of each . (Fill in the blanks) 2.3 cm 3 in. 5 in. C = πd C = π(15) C = 47.1 m A = πr2 A = π(7.5)2 A = 176. 7 m2 *hint: use PT C = πd C = π( ____ ) C = _____cm A = πr2 A = π(2.3)2 A = 16.6 cm2 C = πd C = π( ____ ) C = _____ in. A = πr2 A = π( ____ )2 A = _______in2

Ex. 3) The diameter of a bicycle wheel is 17 inches. If the wheel makes 10,500 revolutions, how far did the bike travel? d = 17; C = πd C = π(17) C ≈ 53.4 For 1 revolution, the bike traveled about 53.4 in. To find the distance traveled for 10,500 revolutions, multiply: C ≈ 53.4 × 10,500 C ≈ 560,774.3 inches