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Circle Concepts and Equations Explanation

Learn circle vocabulary, chord, diameter, equations, and intersecting circles with clear examples and solutions. Improve your circle knowledge now!

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Circle Concepts and Equations Explanation

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  1. Concept 52 Circles and their parts

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

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

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

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

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

  7. 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 = 2rd = 21 10.5 = r Simplify. Answer:QV = 10.5 cm

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

  9. Concept

  10. 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

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

  12. Equations of Circles Concept 53

  13. Concept

  14. 1. Write the equation of the circle with a center at (3, –3) and a radius of 6. (x – h)2 + (y – k)2 = r2 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

  15. 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 = r2 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

  16. 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

  17. 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

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

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

  20. 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 = r2 (x + 3)2 + (y + 2)2 = r2 Plug it in (1 + 3)2 + (-2 + 2)2 = r2 (4)2 + (0)2 = r2 16 = r2 Answer:(x + 3)2 + (y + 2)2 = 16

  21. 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 = r2 (x + 1)2 + (y + 0)2 = r2 Plug it in (3 + 1)2 + (0 + 0)2 = r2 (4)2 + (0)2 = r2 16 = r2 Answer:(x + 1)2 + y2 = 16

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