Circles and coordinate circles
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The document contains various questions and answers related to circles and geometry. It covers definitions of circle properties, calculations involving distances, angles, and areas, as well as the identification and properties of different geometrical figures. Additionally, it includes specific problems related to inscribed angles, secants, tangents, and coordinates of points.
Circles and coordinate circles
- 2. Circles A closed plane whose every point is equidistant from a point within the curve. Answer: circle
- 3. Circles The given point described in the definition of the circle. Answer: center
- 4. Circles The length around a circle. Answer: circumference
- 5. Circles A chord passing through the center of the circle. Answer: diameter
- 6. Circles A segment whose endpoints are points on the circle. Answer: chord
- 7. Circles A line which intersects the circle at exactly one point. Answer: tangent line
- 8. Circles A line which intersects the circle at two points. Answer: secant line
- 9. Circles The set of all points whose distance from the center is less than the radius. Answer: interior of the circle
- 10. Circles The set of all points/ whose distance from the center is greater than the radius. Answer: exterior of the circle
- 11. Circles It is an angle in the circle whose vertex is the center of the circle. Answer: central angle
- 12. Circles An arc with a measure of 180 is a Answer: semicircle
- 13. Circles An inscribed angle of a circle measures 45. What is the measure of its intercepted arc? Answer: 90
- 14. Circles Which of the following ordered pairs is a point of the circle with equation x2 + y2 = 45? a. ( -5,5) b. (3,-6) Answer: b. ( 3, -6 )
- 15. Circles The measure of the central angle of a regular nonagon is. Answer: 40
- 16. Circles The measure of a central angle of a circle is equal to the measure of its intercepted arc. Answer: The Central Angle-Intercepted Arc Postulate
- 17. Circles The measure of an inscribed angle is one-half the measure of its intercepted arc. Answer: The Inscribed Angle Theorem
- 18. Circles Two or more angles inscribed in the same arc are congruent. Answer: The inscribed Angles in the same Arc Theorem
- 19. Circles What is the distance between the points (-2, 5) and (4, -3)? Answer: 10
- 20. Circles What is the distance between the points (3, -7) and (6, 2)? Answer:
- 21. Circles (-3, 2) and (12, 10) are points on opposite ends of the diameter of a circle. What is the radius of the circle? Answer: 8.5
- 22. Circles The distance between the points (-2, y) and (3, -7) is 13 units. What are the possible values for y? Answer: y = -19 or 5
- 23. Circles The coordinates of the right-angled triangle ABC are: A = (1,2), B = (3,6) and C = (7,4). What is the length of the hypotenuse of the triangle? Answer:
- 24. Circles What is the midpoint of the straight line segment joining the points (-2, 5) and (6, -1)? Answer: (2, 2)
- 25. Circles What is the midpoint of AB? Answer:
- 26. Circles What is the midpoint of the straight line segment joining the points (3, -6) and (-4, -3)? Answer:
- 27. Circles What is the midpoint of the straight line segment joining the points (-2, 9) and (3, -2)? Answer:
- 28. Circles What is the midpoint of BC? Answer:
- 29. Circles Find the area of a circle whose circumference is 4𝜋 3 ? Answer: 4𝜋 9
- 30. Circles QP is tangent to circle O at P. If 𝑚∠𝑃𝑂𝑄 = 73, what is 𝑚∠𝑄 ? Answer: 17 O P Q
- 31. Circles PS and PQ are secant and tangent circle A. if arc RQ is 52, what is 𝑚∠𝑃 ? Answer: 26 S R A Q P
- 32. Circles Answer: 85 C A B D E Given circle E with secants AB and CD if arc AC = 53 and arc BD = 117, find 𝑚∠CEA ?
- 33. Circles Answer: 26 P S R Q O A Given circle A with secants OQ and OP if arc RS = 32 and arc QP=84, find 𝑚∠𝑂 ?
- 34. Circles Given 𝐴𝐵 ⊥ 𝐶𝐷 𝑎𝑡 𝐹, CD is 10cm long. How far is CD from the center if the length of the radius is 13 cm. Answer: 12 F AB C D
- 35. Circles Find the circumference of a circle whose radius is 3 𝜋 𝑖𝑛 . Answer: 6
- 36. Circles The radius of a circle is 20. Find the length of the arc whose measure is 45o. Answer: 5π
- 37. Circles What is the center of a circle with equation of x2 +(y+7)2=25 ? Answer: (0, -7)
- 38. Circles What is the equation of the circle whose center is ( -4, -3 ) and passing through the origin ? Answer: (x + 4)2 +(y + 3)2 = 25
- 39. Circles Find the perimeter of a triangle whose vertices are at the given points A(0,-4), B(3,0), C(0,0). Answer: 12 units
- 40. Circles Find the area of a triangle whose vertices are at the given points A(0,-4), B(3,0), C(0,0). Answer: 6 units
- 41. Circles Draw a triangle with vertices A(0,-4), B(3,0), C(0,0). What kind of triangle it is? Answer: right triangle
- 42. Circles If A is a the midpoint MN , determine the coordinates of A if the coordinates of the endpoints are M(-4,-3) and N(4,3). Answer: (0,0)