1. Circles and their parts
Concept 52
Circles and their parts

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

4. 1. Name the circle and identify a radius.

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

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

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

9. 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

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

11. Concept

12. 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
= XY
14 = XY

13. 8.
A. 3 in.
B. 5 in.
C. 7 in.
D. 9 in.

14. Equations of Circles
Concept 53

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

16. 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

17. 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

18. 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

19. 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

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

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

22. (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

23. (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