Lesson 10 1 Introduction to Circles Circles Terms

Lesson 10 -1 Introduction to Circles

Circles - Terms y 90° Di am et e r( 180° d) Radius (r) Center Chord 270° Circumference = 2πr = dπ x 0°

Objectives • Identify and use parts of circles – circle – center – radii, r – chords – diameter (2 r = d): longest chord • Solve problems involving the circumference of a circle – formulas: C = 2πr or C = dπ

Vocabulary • Circle – the locus (set) of all points in a plane equidistant for a given point • Center – the central point of a circle • Chord – any segment that endpoints are on the circle • Diameter – a chord that passes through the center of the circle • Radius – any segment that endpoints are the center and a point on the circle • Circumference – perimeter of a circle

a. Name the circle. Answer: The circle has its center at E, so it is named circle E, or. b. Name the radius of the circle. Answer: Four radii are shown: . c. Name a chord of the circle. Answer: Four chords are shown: . d. Name a diameter of the circle. Answer: are the only chords that go through the center. So, are diameters.

a. Name the circle. Answer: b. Name a radius of the circle. Answer: c. Name a chord of the circle. Answer: d. Name a diameter of the circle. Answer:

Circle R has diameters a. If ST = 18, find RS. and . Formula for radius Substitute and simplify. Answer: 9 b. If RM = 24, find QM. Formula for diameter Substitute and simplify. Answer: 48 c. If RN = 2, find RP. Since all radii are congruent, RN = RP. Answer: So, RP = 2.

Circle M has diameters a. If BG = 25, find MG. Answer: 12. 5 b. If DM = 29, find DN. Answer: 58 c. If MF = 8. 5, find MG. Answer: 8. 5

The diameters of and are 22 millimeters, 16 millimeters, and 10 millimeters, respectively. Find EZ.

Since the diameter of , EF = 22. Since the diameter of FZ = 5. is part of . Segment Addition Postulate Substitution Simplify. Answer: 27 mm

The diameters of and are 22 millimeters, 16 millimeters, and 10 millimeters, respectively. Find XF. Since the diameter of is part of . Since Answer: 11 mm , EF = 22. is a radius of

The diameters of , and are 5 inches, 9 inches, and 18 inches respectively. a. Find AC. Answer: 6. 5 in. b. Find EB. Answer: 13. 5 in.

a. Find C if r = 13 inches. Circumference formula Substitution Answer: b. Find C if d = 6 millimeters. Circumference formula Substitution Answer:

Find d and r to the nearest hundredth if C = 65. 4 feet. Circumference formula Substitution Divide each side by. Use a calculator. Radius formula Use a calculator. Answer:

a. Find C if r = 22 centimeters. Answer: b. Find C if d = 3 feet. Answer: c. Find d and r to the nearest hundredth if C = 16. 8 meters. Answer:

Summary & Homework • Summary: – Diameter of a circle is twice the radius – Circumference, C, of a circle with diameter, d, or a radius, r, can be written in the form C = πd or C = 2πr • Homework: pg 526 -527; 16 -20, 32, 33, 44 -47