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Circle Equations and Geometry Concepts

This chapter covers the standard equation of a circle, determining circle equations, tangent and secant lines, properties of chords and arcs, and more.

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Circle Equations and Geometry Concepts

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  1. Chapter 10 Jeopardy By: Ryan Gorman, Matt Margulies, Rishab Lal, and Gabe Shindnes

  2. 10.1 10.2 10.3 10.4 10.5 10.6 10.7 100 100 100 100 100 100 100 200 200 200 200 200 200 200 300 300 300 300 300 300 300 400 400 400 400 400 400 400 500 500 500 500 500 500 500 FINAL JEOPARDY! FINAL JEOPARDY!

  3. FINAL JEOPARDY!

  4. FINAL JEOPARDY! Question How many licks does it take to get to the center of a tootsie pop?

  5. FINAL JEOPARDY! Answer 4

  6. 10.7100 Write the standard equation of a circle with center (0,-9) and radius 4.2.

  7. x² + (y + 9) = 17.64

  8. 10.7200 The standard equation of a circle can be written for any circle with know ____ and ____.

  9. Center, Radius

  10. 10.7300 Determine whether the given equation defines a circle. If the equation defines a circle, rewrite the equation in standard form: x² + y² - 6y + 9 = 4

  11. Circle; x² + (y – 3)² = 4

  12. 10.7400 Use the given equation of a circle and a line to determine whether the line is a tangent, secant, secant that contains a diameter, or none of these: Circle: (x - 4)² + (y - 3)² = 9 Line: y = -3x + 6

  13. Secant

  14. 10.7500 The diameter of a CD is about 4.8 inches. The diameter of the hole in the center is about 0.6 inches. You place a CD on the coordinate plane with center at (0,0). Write the equations for the outside edge of the disc and edge of the hole in the center.

  15. x² + y² = 5.76 x² + y² = 0.09

  16. 10.6400 • A perpendicular bisector passes through the center and bisects a chord. The length of the diameter is 2 and 2x+6, and the chord is bisected with an x length and another x length, what is the value of x?

  17. 10.4400 • X=6

  18. 10.6500 • If chord AB intersects chord CD at point E inside the circle and AE has a length of x+2, BE has a length of x+1, CE has a length of x+4, and DE has a length of x, what is the value of x?

  19. 10.6500 • 2

  20. 10.6300 • If a tangent meets point E and a secant meets at point E, what is the relationship of the tangent in secant?

  21. 10.6300 • EA²=EC x ED

  22. 10.6200 • If secant AB and secant CD meet at point E outside the circle and EA has a length of 3, EC has a length of 4, AB has a length of 8, what is the length of CD?

  23. 10.6200 • 6

  24. 10.6100 • If chord AB intersects chord CD at point E inside the circle and AE has a length of 6, BE has a length of 7, CE has a length of 10, what is the length of DE?

  25. 10.6100 • 4.2

  26. 10.5500 • You’re flying on a plane 1.2 miles above the ground. Figure out the measure of the arc that represents the part of Earth that you can see.

  27. 10.5500 • About 2.8°

  28. 10.5400 • Circle EFG is inscribed in Triangle PQR. If angle Q is 60°, angle P is 40°, and angle R is 80°, what is the measure of arc EG, FG, and GE?

  29. 10.5400 • 120°,100°,and 140°

  30. 10.5300 • If tangent AB and secant CD meet at A and arc AC is 40° and arc AD is 70°, what is the measure of angle BAC?

  31. 10.5300 • 55°

  32. 10.5200 • In a circle chords AB and CD intersect at point E. If arc AB is 40° and CD is 90°, then what is the angle of AEB?

  33. 10.5200 • 65°

  34. 10.5100 • In circle A chord BC meets at tangent DE. If angle BCD is 40°, what is the measure of arc BC?

  35. 10.5100 • 80°

  36. 10.4500 • If central angle ADC is 60° then what is the measure of inscribed angle ABC?

  37. 30°

  38. 10.4400 • If inscribed angle EFG is (8x+10)° and arc EG is (12x+40)° then what is x?

  39. 5

  40. 10.4300 • If quadrilateral EFGH is inscribed in circle Z and angle E is 73° then what is the measure of angle G?

  41. 107

  42. 10.4200 • If there is a right triangle inscribed in a circle then the hypotenuse is the ________ of the circle.

  43. Diameter

  44. 10.4100 • If the inscribed angle ABC is 63° then what is the measure of arc AB?

  45. 126

  46. 10.3500 • If AB and DC are equidistant to the center of circle E and AB is 3x²-9 and DC is 3x+9 what is x?

  47. -2

  48. 10.3400 • If chord AB and chord CB are congruent and arc AC is 130° then what are the measure of arc AB and arc CB?

  49. AB and BC both are 115°

  50. 10.3300 • If chord DE and chord BA are equidistant to the center of circle C and arc BA is 135° then what is the measure of arc DE?

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