Name: ___________________________
Block: ___________
CH 10 PRACTICE PROBLEMS
Prerequisite Skills: 1. Vertical and supplementary angles 2. Pythagorean Theorem
Notes
Assignment
Score
Learning Target(s)
What am I confident about?
Where do I need to spend more time?
Am I weak on a prerequisite skill?
What am I going to do if I am weak?
10.1/10.7
30
10.2/10.3
52
10.4/10.5
44
10.1-10.5, 10.7
Review
39
10.6
25
Learning Targets:







Use properties of a tangent to a circle
Use angle measures to find arc measures
Use relationships of arcs and chords in a circle
Use inscribed angles of circles
Find the measures of angles inside or outside a circle
Find segment lengths in circles
Write equations of circles in the coordinate plane
~ April 2015 ~
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Sun
Mon
Tue
Wed
►
Thu
Fri
27 A
Sat
28
10.1, 10.7 Properties of
Circles
HW 10.1, 10.7
SOL G.12
29
30
31
1
2
3
4
5
6
7B
8A
9B
10 A
11
10.1, 10.7 Properties of
Circles
10.2-10.3 Arcs and
Chords
10.2-10.3 Arcs and
Chords
10.4-10.5 Inscribed
Angles and Circles
HW 10.1, 10.7
SOL Review G.7,G.8
HW 10.2-10.3
HW 10.2-10.3
SOL Review G.3
HW 10.4-10.5
13 B
14 A
15 B
Review 10.1-10.5, 10.7
Review 10.1-10.5, 10.7
16 A
***Quiz***
10.1-10.5,10.7
17 B
***Quiz***
10.1-10.5,10.7
18
10.4-10.5 Inscribed
Angles and Circles
HW 10.4-10.5
SOL Review G.12
HW Quiz Review
HW Quiz Review
20 A
21 B
22 A
23 B
24 A
25
10.6 Segments and
Circles
10.6 Segments and
Circles
HW 10.6
HW 10.6
12
19
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Practice Problems: 10.1 Tangents and Chords
Match the notation with the term that best describes it.
______1. D
A. Center
⃡
______2. 𝐹𝐻
B. Chord
______3. ̅̅̅̅
𝐶𝐷
C. Diameter
______4. ̅̅̅̅
𝐴𝐵
D. Radius
______5. C
E. Point of Tangency
̅̅̅̅
______6. 𝐴𝐷
F. Common External Tangent
⃡
______7. 𝐴𝐵
G. Common Internal Tangent
______8. ⃡𝐷𝐸
H. Secant
49
Use the diagram at the right.
9. What are the diameter and radius of ⊙ A?
10. What are the diameter and radius of ⊙B?
11. Describe the intersection of the two circles.
12. Describe all the common tangents of the two circles.
Use ⊙ P to draw part of the circle described to answer the question.
13. Draw a diameter ̅̅̅̅
𝐴𝐵.
14. Draw tangent line ⃡𝐶𝐵.
15. Draw chord ̅̅̅̅
𝐷𝐵.
16. Draw a secant through point A.
17. What is the name of a radius in the figure?
Tell how many common tangents the circles have and draw them.
18.
19.
20.
Draw two circles with the given number of common tangents.
21. 3
22. 2
23. 1
̅̅̅̅ is tangent to ⊙C. Explain your reasoning.
In the diagram, ̅̅̅̅
𝑩𝑪 is a radius of ⊙ C. Determine whether 𝑨𝑩
24.
25.
̅̅̅̅ is tangent to ⊙ C at point B. Find the radius r of ⊙C.
In the diagram, 𝑨𝑩
26.
27.
̅̅̅̅ is tangent to ⊙L at K and 𝑱𝑴
̅̅̅̅ is tangent to ⊙ L at M. Find the value of x.
𝑱𝑲
28.
29.
30. Softball On a softball field, home plate is 38 feet from the pitching circle. Home plate is about 45.3 feet from a
point of tangency on the circle.
a. How far is it from home plate to a point of tangency on the other side of the
pitching circle?
b. What is the radius of the pitching circle?
Practice Problems: 10.7 Equation of a Circle
Match the equation of a circle with its description
1. x 2  y 2  4
2.
x2  y 2  9
3.
( x  1)2  ( y  4)2  16
4.
( x  2)2  ( y  3) 2  9
5.
( x  3)2  ( y  5)2  16
6.
( x  2)2  ( y  5) 2  9
A.
B.
C.
D.
E.
F.
Center (-1,4), radius 4
Center (-2,-3), radius 3
Center (0,0), radius 2
Center (2,5), radius 3
Center (-3,5), radius 4
Center (0,0), radius 3
Give the center and radius of the circle.
7.
x 2  ( y  4)2  9
8.
( x  1)2  ( y  1)2  4
Write the standard equation of the circle.
9.
12.
Write the standard equation of the circle with given center and radius.
13. Center (2,0), radius 3
14. Center(5,-6), radius 1
Use the given information to write the standard equation of the circle.
15. The center is (-1, 2), and a point on the circle is (2, 6).
Graph the equation. Pay close attention to the scale of each graph.
16. x 2  y 2  25
18. x 2  ( y  2)2  9
17. ( x  1)2  y 2  4
19. ( x  3)2  ( y  1)2  4
Practice Problems: 10.2 Arc Measures and 10.3 Apply Properties of
Chords
52
Practice Problems: 10.4 Inscribed Angles and 10.5 Apply Other Angle
Relationships in Circles
44
10.5 Apply Other Angle Relationships in Circles
Practice Problems: 10.1-10.5, 10.7 Quiz Review
39
9. Determine if AB is tangent to circle C. Explain your reasoning.
10. In each diagram, solve for the radius. Segment AB is tangent to circle C.
11. In each diagram, JK and JM are tangent to the circle. Solve for the variable.
In each diagram, solve for the missing arc or angle.
27.
28.
29.
30.
33.
31.
34.
36.
37.
38. In the diagram, solve for the missing variables.
39. Solve for x.
32.
35.
Practice Problems: 10.6 Find Segment Lengths in Circles
25
Ch 10 Review Practice Problems
36
Find the value of x for questions #1 – 3.
1.)
2.)
3.)
4.) In the figure, ̅̅̅̅
𝑃𝑅 and ̅̅̅̅
𝑄𝑆 are diameters of U. Find the measure of the indicated arc.
a. mPQ
b. mST
c. mTPS
d. mRT
e. mRQS
f. mQR
g. mPQS
h. mTQR
i. mPS
j. mPTR
Find the value of x for questions #5 – 6.
5.)
6.)
7.) Find the indicated measure in O
, given mCD = 85° and mBE = 97°.
a. mABC
b. mCED
c. mBDE
d. mCBD
e. mABD
f. mBCE
g. mAD
h. mABC
8.) Find mAC.
10.) Find mA.
9.) Find mBC.
11.) Find mAB
Find the m1 for questions #12 – 14.
12.)
13.)
14.)
Find the value of x for questions #15 – 22.
15.)
16.)
17.)
18.)
19.)
20.)
21.)
22.)
Word Problems: Draw a picture to help you answer each problem.
23. A right triangle is inscribed in a circle of radius 9. The length of the hypotenuse of the right triangle is
.
24. Points A, B, C, and D, in that order, are on the same circle. If m∠ABC is 115°, then m∠CDA is
.
25. Points A and B are on a circle. Point C lies outside of the circle such that ⃡𝐴𝐶 is tangent to the circle and BAC is
acute. If mAB is 110°, then mBAC is
.
26. Points A, B, C, and D, in that order, are on the same circle. ̅̅̅̅
𝐴𝐶 intersects ̅̅̅̅
𝐵𝐷 at the point E. If the length of ̅̅̅̅
𝐵𝐸 is
̅̅̅̅ is __ .
̅̅̅̅ is 4, and the length of ̅̅̅̅
7, the length of 𝐷𝐸
𝐴𝐸 is 3, then the length of 𝐴𝐶
Match the definition with the corresponding term. Use CAPITAL letters.
A. Arc
F.
B. Chord
G.
C. Congruent circles
H.
D. Circle
I.
E. Diameter
_____ 27. Part of the circle between any two points on the circle.
Radius
Secant
Semicircle
Tangent
_____28. A chord that contains the center of the circle.
_____ 29. Any segment that joins the center to a point on the circle.
_____ 30. A line in the plane of the circle that intersect the circle in exactly one point
_____ 31. A line that intersects the circle in two points.
_____ 32. A line segment with both endpoints on the circle.
_____ 33. The set of all points in a plane at a given distance from a fixed point
_____ 34. Circles with congruent radii.
_____ 35. An arc with endpoints that are also the endpoints of a diameter.
36.