Circles and their parts Concept 52 Circles and their parts

Vocabulary Circle – the set of all points equidistant from a center.

1. Name the circle and identify a radius.

2. Identify a chord and a diameter of the circle.

3. Name the circle and identify a radius. B. C. D.

4. Which segment is not a chord? B. C. D.

5. If RT = 21 cm, what is the length of QV? RT is a diameter and QV is a radius. d = 2r Diameter Formula 21 = 2r d = 21 10.5 = r Simplify. Answer: QV = 10.5 cm

6. If QS = 26 cm, what is the length of RV? A. 12 cm B. 13 cm C. 16 cm D. 26 cm

Concept

7. First, find ZY. WZ + ZY = WY 5 + ZY = 8 ZY = 3 Next, find XY. Find Measures in Intersecting Circles 7. First, find ZY. WZ + ZY = WY 5 + ZY = 8 ZY = 3 Next, find XY. XZ + ZY = XY 11 + 3 = XY 14 = XY

8. A. 3 in. B. 5 in. C. 7 in. D. 9 in.

Equations of Circles Concept 53

Concept 𝑟= 𝑥 1 − 𝑥 2 2 + 𝑦 1 − 𝑦 2 2 𝑟= 𝑥−ℎ 2 + 𝑦−𝑘 2 𝑟= 𝑥 1 − 𝑥 2 2 + 𝑦 1 − 𝑦 2 2 𝑟= 𝑥−ℎ 2 + 𝑦−𝑘 2 𝑟 2 = 𝑥−ℎ 2 + 𝑦−𝑘 2

1. Write the equation of the circle with a center at (3, –3) and a radius of 6. (x – h)2 + (y – k)2 = r 2 Equation of circle (x – 3)2 + (y – (–3))2 = 62 Substitution (x – 3)2 + (y + 3)2 = 36 Simplify. Answer: (x – 3)2 + (y + 3)2 = 36

2. Write the equation of the circle graphed to the right. The center is at (1, 3) and the radius is 2. (x – h)2 + (y – k)2 = r 2 Equation of circle (x – 1)2 + (y – 3)2 = 22 Substitution (x – 1)2 + (y – 3)2 = 4 Simplify. Answer: (x – 1)2 + (y – 3)2 = 4

3. Write the equation of the circle with a center at (2, –4) and a radius of 4. A. (x – 2)2 + (y + 4)2 = 4 B. (x + 2)2 + (y – 4)2 = 4 C. (x – 2)2 + (y + 4)2 = 16 D. (x + 2)2 + (y – 4)2 = 16

4. Write the equation of the circle graphed to the right. A. x2 + (y + 3)2 = 3 B. x2 + (y – 3)2 = 3 C. x2 + (y + 3)2 = 9 D. x2 + (y – 3)2 = 9

5. List the center and radius length of the circle with the formula x2 + (y + 3)2 = 9. (0, -3) R = 3

6. List the center and radius length of the circle with the formula (x + 3)2 + (y – 2)2 = 18  

(x – h)2 + (y – k)2 = r 2 (x + 3)2 + (y + 2)2 = r 2 7. Write the equation of the circle that has its center at (–3, –2) and passes through (1, –2). (x – h)2 + (y – k)2 = r 2 (x + 3)2 + (y + 2)2 = r 2 Plug it in (1 + 3)2 + (-2 + 2)2 = r 2 (4)2 + (0)2 = r 2 16 = r 2 Answer: (x + 3)2 + (y + 2)2 = 16

(x – h)2 + (y – k)2 = r 2 (x + 1)2 + (y + 0)2 = r 2 8. Write the equation of the circle that has its center at (–1, 0) and passes through (3, 0). (x – h)2 + (y – k)2 = r 2 (x + 1)2 + (y + 0)2 = r 2 Plug it in (3 + 1)2 + (0 + 0)2 = r 2 (4)2 + (0)2 = r 2 16 = r 2 Answer: (x + 1)2 + y 2 = 16