Aim: What are the parts of a circle



Aim 11: What are the parts of a circle?

Do Now: Match each definition with the correct term, and write it on the line.

arc, center, central angle, chord, circle, congruent arcs, congruent circles,

diameter, major arc, minor arc, radius, secant, semicircle, tangent

_________________ 1. A set of points in a plane such that the points are equidistant from a fixed point called the center.

_________________ 2. A line segment from the center of the circle to any point on the circle.

_________________ 3. A line segment connecting two points on the circle,

and passes through the center.

_________________ 4. The given point from which all points on the circle are equidistant.

_________________ 5. A line segment whose endpoints are points of the circle.

_________________ 6. A line in the plane of the circle that intersects the circle in

exactly one point.

_________________ 7. A line that intersects the circle in two points.

_________________ 8. An angle whose vertex is the center of the circle.

_________________ 9. Any part of the circle.

_________________ 10. A half of a circle as divided by a diameter.

_________________ 11. An arc whose measure is less than a semicircle.

_________________ 12. An arc whose measure is more than a semicircle.

_________________13. Circles with congruent radii.

_________________14. Arcs of the same or congruent circles that are equal in measure.

Use the accompanying diagram to answer the following questions for circle B:

Write your answer on the line, do not circle. A, C, D, G, E, F, & H are points on the circle B, and passes through B.

_____ 15. Which of the following is a major arc of circle B?

(1) (2) (3) (4)

_____ 16. Which of the following is NOT a chord of circle B?

(1) (2) (3) (4)

_____ 17. Which of the following is NOT a central angle of circle B? (1) [pic]DBE (2) [pic]ABF (3) [pic]CAF (4) [pic]CBD

_____ 18. Which of the following is a minor arc of circle B?

(1) (2) (3) (4)

Examine the given measurements. A, C, D, G, E, F, & H are points on the circle B, and [pic] passes through B.

Complete the following questions, including the theorem in each box.

1. What is the difference between arc degrees and arc length?

2. In the same circle or congruent circles all radii are ___________________________.

3. The degree measure of a central angle of a circle is __________ to the measure of its

intercepted arc.

4. (a) What kind of angle is [pic]CBF? (b) What can we say about [pic]ABC and [pic]ABF?

5. (a) What should the sum of the measures of [pic]ABC & [pic]ABF be? _____________

(b) What should [pic] be? _______________

(c) Why do you think the measurements are off?

6. What do all of the central angles 7. What do all of the arcs add

add up to? _______ up to? _______

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Based on the diagram below, answer the questions given. [pic]and [pic] pass through O of circle O.

8. Name 4 central angles. _____ , _____ , _____ , _____

9. Name both diameters. _____ , _____

10. Name the 5 radii. _____, _____, _____, _____, _____

11. Name 3 chords. _____ , _____ , _____

12. Name 4 minor arcs using 3 points. _____ , _____ , _____ , _____

13. Name 4 minor arcs using 2 points. _____ , _____ , _____ , _____

14. Name 4 major arcs using 3 points. _____ , _____ , _____ , _____

Find the measure of each:

15. m[pic]POM = _____ 16. m [pic]POJ = _____ 17. = _____ 18. = _____

19. = _____ 20. m [pic]MOJ = _____ 21. m[pic]NOJ = _____ 22. [pic] = _____

23. [pic] = _____ 24. = _____ 25. m[pic]ROJ = _____ 26. = _____

27. What kind of triangle is MOP? 28. What kind of triangle is ROP?

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