Circles Chapter 10.1

Identify and use parts of circles. Solve problems involving the circumference of a circle. circle diameter circumference pi () center chord radius Standard 8.0 Students know, derive, and solve problems involving the perimeter, circumference, area, volume, lateral area, and surface area of common geometric figures. (Key) Lesson 1 MI/Vocab

Circle Terms Def: The set of all points a given distance from a given point. The given point is the Center The given distance is the Radius A circle with center P is called “circle P” or P

Circle Distances The distance from the center to any point on the circle is called the radius All radii of a circle are congruent All circles with equal radii are congruent The distance across the circle, through its center, is the diameter of the circle The diameter is twice the radius The distance around the circle is called the circumference. C = 2πr or C = πd

Find Radius and Diameter Formula for radius Substitute and simplify. Answer: 9 Lesson 1 Ex2

Find Radius and Diameter Since all radii are congruent, RN = RP. Answer: So, RP = 2. Lesson 1 Ex2

A. 6.25 B. 12.5 C. 25 D. 50 A B C D Lesson 1 CYP2

A. 7.25 B. 14.5 C. 29 D. 58 A B C D Lesson 1 CYP2

A. 4.25 B. 8.5 C. 17 D. 85 A B C D Lesson 1 CYP2

Find Measures in Intersecting Circles 10 22 5 22 + 5 = 27 Lesson 1 Ex3

A. 2.5 in. B. 4.5 in. C. 6.5 in. D. 9 in. A B C D Lesson 1 CYP3

A. 13.5 in. B. 15.5 in. C. 13 in. D. 12.5 in. A B C D Lesson 1 CYP3

It takes just over three diameters to wrap around a circle.

π and Circumference Circumference: The distance around a circle C = 2πr or C = πd Pi  π = irrational number In this class, leave all answers in terms of π Ex: 5π or

A. Find C if r = 13 inches. Answer: 26 or ≈ 81.68 in. Find Circumference, Diameter, and Radius A. Find C if r = 13 inches. Circumference formula Substitution Answer: 26 or ≈ 81.68 in. Lesson 1 Ex4

B. Find C if d = 6 millimeters. Find Circumference, Diameter, and Radius B. Find C if d = 6 millimeters. Circumference formula Substitution Answer: 6 or ≈ 18.85 mm Lesson 1 Ex4

C. Find d and r to the nearest hundredth if C = 65.4 feet. Find Circumference, Diameter, and Radius C. Find d and r to the nearest hundredth if C = 65.4 feet. Circumference formula Substitution Divide each side by . Use a calculator. Lesson 1 Ex4

A. 44 cm. B. 69.12 cm C. 22 cm D. 138.23 cm A B C D Lesson 1 CYP4

A. 1.5 ft B. 3 ft C. 9.42 ft D. 18.85 ft A B C D Lesson 1 CYP4

A. 8.4 m B. 5.35 m C. 2.67 m D. 16.8 m A B C D Lesson 1 CYP4

Segments and Lines Radius—a segment from the center to any point on the circle Chord—a segment whose endpoints are on the circle Diameter—a chord that passes through the center of the circle Secant—a line that intersects a circle in two points Tangent—a line that intersects the circle in only one point

Secant Tangent Diameter Radius Point of Tangency Chord

Identify Parts of a Circle A. Name the circle. Lesson 1 Ex1

Identify Parts of a Circle B. Name a radius of the circle. Lesson 1 Ex1

Identify Parts of a Circle C. Name a chord of the circle. Lesson 1 Ex1

Identify Parts of a Circle D. Name a diameter of the circle. Lesson 1 Ex1

A. Name the circle. A. B. C. D. A B C D Lesson 1 CYP1

B. Name a radius of the circle. Lesson 1 CYP1

C. Name a chord of the circle. B. C. D. A B C D Lesson 1 CYP1

D. Name a diameter of the circle. B. C. D. A B C D Lesson 1 CYP1

Concentric Circles Circles with the same Center but different radii

Special Right Triangle!!! Use Other Figures to Find Circumference x Special Right Triangle!!! 45o- 45o-90o x = 3 = radius C = 2π(3) = 6π Lesson 1 Ex5

A. B. C. D. A B C D Lesson 1 CYP5

Homework (get it?) Chapter 10-1 Pg 557 # 13 – 52 all, & 60 Yes, it is a lot of problems but they are very quick.