Geometry
Name_________________________________________hr ____
Ch 10 Notes Sections 10.1 – 10.3
Date _____/_____/_____ Score:
%
Answer each of the following .
A
1. The circle’s center is _____ because ________________________________
B
D
.
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2. A circle is named by its ______________. This circle’s name is ___________
C
E
3. _________ is a diameter of the circle because _________________________
R
_______________________________________________________________
4. ________ is a radius of the circle because ____________________________
_________________________________________________________________
5. ________ is a chord of the circle because _____________________________________________________________.
6. The diameter of a circle is always ___________________ the circle’s radius.
7. The distance around a circle is called its __________________________________________ ; the formulas for this are
___________________ and _________________________. The total number of degrees around a circle is __________
8. The formula for the area of a circle is ____________________.
9. Define and draw each type of arc of a circle.
In general, an arc is ___________________________________________________________.
A minor arc is _______________________________________________________________.
A minor arc is named by ______________________________________________________ .
A semicircle is _____________________________________________ and is named by __________________________.
A major arc is ________________________________________________________ and is named by _______________
_________________________________________________________________________________________________.
10. Define and draw a central angle.
An angle is a central angle when ______________________________________
_________________________________________________________________
_________________________________________________________________
11. Find the measure of each central angle. Highlight the angle’s intercepted arc.
12. What conjectures might you make about the degree measure of a central angle compared to it intercepted arc?
_________________________________________
Formula:
13. In your own words, what does the arc addition postulate tell you about the addition of arcs ? (include a diagram)
___________________________________________________________________
___________________________________________________________________
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14. Is the length of an arc the same as its degree measure? __________ Arc length is a fraction of the circle’s
____________________________________________ whereas arc degree is a fraction of ______________.
15. How would the ratio of arc length to circumference compare to the ratio of arc degree measure to 360.
__________________________________________________________________________________________________
16. Write a formula comparing arc length to arc degree measure.
17. Highlight the arcs that correspond to the following chords.
A
A
E
C
C
B
D
A
E
A
E
C
B
D
E
C
B
B
D
D
18. Draw the chords that correspond to AB.
A
A
A
C
C
B
B
B
19. What does theorem 10.2 tell you about the relationship between congruent chords and arcs in problem 18?
20. In
X, draw the diameter perpendicular to each of the following chords. Mark the point of intersection P. Find the
indicated measures.
A
A
E
C
E
C
E
C
B
B
D
A
B
D
D
CP = _________
AP = _________
CP = _________
EP = _________
BP = _________
DP = _________
mCPX = ________
mAPX = ________
mCPX = ________
What do relationships do you see?
21. Define inscribed polygons and draw 2 examples.
Definition:
21. Define circumscribed polygons and draw 2 examples.
Definition:
23. Compare and contrast inscribed and circumscribed poygons?
24. Draw two congruent chords in the circle provided. What can you tell me about
their distances from the center?