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Circles

Math · Geometry and Trigonometry · 29 questions · every one comes with a full explanation.

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  1. 1The circle above has center O, the length of arc is , and . What is the length of arc ?Hard · Geometry and Trigonometry
  2. 2The graph of x 2 + x + y 2 + y = 199 2 in the xy-plane is a circle. What is the length of the circle's radius?Hard · Geometry and Trigonometry
  3. 3The equation above defines a circle in the xy-plane. What are the coordinates of the center of the circle?Hard · Geometry and Trigonometry
  4. 4Point O is the center of the circle above, and the measure of is . If the length of is 18, what is the length of arc ?Hard · Geometry and Trigonometry
  5. 5A circle in the xy-plane has a diameter with endpoints 2,4 and 2,14. An equation of this circle is x - 2 2 + y - 9 2 = r 2 , where r Hard · Geometry and Trigonometry
  6. 6Circle A in the xy-plane has the equation x + 5 2 + y - 5 2 = 4 . Circle B has the same center as circle A. The radius of circle B is two tHard · Geometry and Trigonometry
  7. 7What is the diameter of the circle in the xy-plane with equation x - 5 2 + y - 3 2 = 16 ?Hard · Geometry and Trigonometry
  8. 8Point O is the center of a circle. The measure of arc R S on this circle is 100°. What is the measure, in degrees, of its associated angle ROS?Hard · Geometry and Trigonometry
  9. 9The equation defines a circle in the xy‑plane. What is the radius of the circle?Hard · Geometry and Trigonometry
  10. 10A circle in the xy-plane has its center at -4,-6. Line k is tangent to this circle at the point -7,-7. What is the slope of line k ?Hard · Geometry and Trigonometry
  11. 11The number of radians in a 720-degree angle can be written as , where a is a constant. What is the value of a ?Medium · Geometry and Trigonometry
  12. 12A circle has center O , and points R and S lie on the circle. In triangle O R S , the measure of ∠ROS is 88°. What is the measure of ∠RSO, in degrees? (Disregard the degree Hard · Geometry and Trigonometry
  13. 13In the xy-plane, the graph of is a circle. What is the radius of the circle?Hard · Geometry and Trigonometry
  14. 14An angle has a measure of 9π20 radians. What is the measure of the angle in degrees?Medium · Geometry and Trigonometry
  15. 15An angle has a measure of 16 π 15 radians. What is the measure of the angle, in degrees?Medium · Geometry and Trigonometry
  16. 16The circle above with center O has a circumference of 36. What is the length of minor arc ?Easy · Geometry and Trigonometry
  17. 17The measure of angle R is 2 π 3 radians. The measure of angle T is 5 π 12 radians greater than the measure of angle R . What is the measure of angle TMedium · Geometry and Trigonometry
  18. 18The equation x 2 + y - 1 2 = 49 represents circle A. Circle B is obtained by shifting circle A down 2 units in the xy-plane. Which of the followingHard · Geometry and Trigonometry
  19. 19A circle has center O , and points A and B lie on the circle. The measure of arc A B is 45∘ and the length of arc A B is 3 inches. What is the circumference, in inchesHard · Geometry and Trigonometry
  20. 20In the xy-plane, a circle with radius 5 has center . Which of the following is an equation of the circle?Medium · Geometry and Trigonometry
  21. 21Which of the following equations represents a circle in the xy-plane that intersects the y-axis at exactly one point?Hard · Geometry and Trigonometry
  22. 22In the xy-plane, the graph of the equation above is a circle. Point P is on the circle and has coordinates . If is a diameter of the circle, what are the coordinates of point Q ?Hard · Geometry and Trigonometry
  23. 23A circle in the xy-plane has its center at -5,2 and has a radius of 9 . An equation of this circle is x2+y2+ax+by+c=0, where a , b , and c are constants. What is the value of c ?Hard · Geometry and Trigonometry
  24. 24The equation x 2 + y - 2 2 = 36 represents circle A. Circle B is obtained by shifting circle A down 4 units in the xy-plane. Which of the followingHard · Geometry and Trigonometry
  25. 25In the xy-plane above, points P, Q, R, and T lie on the circle with center O. The degree measures of angles and are each 30°. What is the radian measure of angle ?Medium · Geometry and Trigonometry
  26. 26The center of the circle is point upper O. Points upper S, upper R, upper Q, and upper P are on the circle. Line segment upper P upper R is a diameter of the circle. Line segment uMedium · Geometry and Trigonometry
  27. 27Points A and B lie on a circle with radius 1, and arc has length . What fraction of the circumference of the circle is the length of arc ?Hard · Geometry and Trigonometry
  28. 28A circle in the xy-plane has equation . Which of the following points does NOT lie in the interior of the circle?Hard · Geometry and Trigonometry
  29. 29A circle in the xy-plane has its center at -4,5 and the point -8,8 lies on the circle. Which equation represents this circle?Medium · Geometry and Trigonometry