Chapter 10: Circles
Assignment Packet
10.1-10.4
Section Assignments
10.1
10.2
10.3
Pg 443:
Pg 447:
Pg 454:
Pg 455:
Pg 463:
Pg 463:
10.4
10.1 The Circle
5, 6, 8, 11, 12, 14, 15, 17, 24
2, 6, 8, 11, 12, 13
1 – 4, 9a, 10a, 11
6, 8, 9d, 10b, 19
1-3, 5, 6, 9, 10, 16
12, 14, 22, 25, 27
Read pages 439-442 (including Sample problems)
Defn:
Circle –
Defn:
Radius –
Defn:
Concentric Circles –
Defn:
Congruent Circles –
Defn:
Interior/Exterior/On –
Defn:
Chord –
Defn:
Diameter –
Special Formulas:
Area
Perimeter
Radius-Chord Relationships Complete the theorems.
Theorem: If a radius is perpendicular to a chord, then _______________________________________
Theorem: If a radius of a circle bisects a chord that is not a diameter, then_____________________________.
Theorem: The perpendicular bisector of a chord passes through_______________________________________.
Examples
1. Given O
AO = 5
DB = 2
Find OC, OD, CD
2. Given O
RT = 12
radius = 10
How far is the chord
from the center?
Use the diagram below to answer questions 1-14
3. Given O
OT = 15
radius = 17
Find AB
10.2 Congruent Chords
Read pages 446-447 (including Sample problems)
Theorem: If 2 chords are equidistant from the center of the circle, then____________________________
Theorem: If 2 chords are congruent, then _____________________________________________________________.
Examples:
Given: O, AB  CD
OP = 12x – 5, OQ = 4x + 19
Find OP
Given: ABC is isosceles, with base AC
P, PQ  AB, PR  CB
Prove: PQR is isosceles
10.3 Arcs of a Circle
Defn:
Arc–
Defn:
Minor Arc –
Defn:
Major Arc–
Defn:
Semi-Circle –
Defn:
Central Angle –
Defn:
Congruent Arcs –
Read pages 450-454 (including Sample problems)
congruent central angles
Examples
1.
2.
Given: B;
D is the midpoint
Prove: BD bisects <ABC
 congruent intercepted arcs  congruent chords
10.4 Secants and Tangents
Defn:
Secant–
Defn:
Tangent–
Defn:
Point of Tangency–
Defn:
Tangent segment–
Defn:
Secant Segment–
Defn:
External part–
Defn:
Tangent circles–
Read pages 450-454 (including Sample problems)
externally tangent–
internally tangent–
Defn:
Common tangent–
Defn:
Tangent circles–
external tangent–
internal tangent–
Theorem: Two-Tangent Theorem________________________________________________________________________
Walk-around problems
Given: Each side of quad ABCD is tangent
to the circle.
AB = 10, BC = 15, AD = 18
Find CD
Common Tangent Procedure
1.
2.
3.
4.
5.
6.
Draw an appropriate diagram
Draw the line of centers
Draw the radii to the points of contact
Through the center of the smaller circle, draw a line parallel to the common tangent
Extend any radius if necessary to obtain right triangles and rectangle.
Use the Pythagorean Theorem and properties of a rectangle.
A. Circles O and P are tangent to each other and have a common external tangent AB. If the radius
of O is 8 and the radius of P is 18, find the length of the common tangent.
B. Circles O and P have a common internal tangent. The radius of O is 1 and the radius of P is 2.
If the distance between their centers is 5, find the length of the common tangent.
C. Circles O and P have a common external tangent. Their centers are 39 cm apart. If the radius of
the smaller circle is 25 and the length of the common tangent is 36, find the radius of the larger
circle.
D. Circles O and P have a common internal tangent. The radius of O is 4 and the radius of P is 3.
If the distance between their centers is 7 , find the length of the common tangent.
Chapter 10: Circles
Assignment Packet
10.1-10.4
Section Assignment Answers
10.1
5. Distance from AB to P = 8mm
9.
statements
1. Given
2. DA  CB
3. ABCD is
6. CD = 16
reasons
1. Given
2. All radii 
3. 2 sides  and 
12. OS = 15
15.
8. C = 24.5cm A = 47.8 cm
11. CD = 8m
14. Radius of other circle = 20
statements
1. Given
2. PQ  PT
3. <PQT  <PTQ
4. <PQT  <PRS
5. <PTS  <PSR
6. <PRS  <PSR
7. PR  PS
8. QR TS
reasons
1. Given
2. All radii 
3. If sides then angles
4. Corr <’s 
5. Corr <’s 
6. Transitive
7. If angles then sides
8. Subtraction
17. a. 13
b. 5
c. 24
10.2
23. PS = 2
8.
statements
1. Given
2. RS  ST
3. SP  SP
4. <QSR is rt <
5. <QST is rt <
6. <QSR  <QST
7. PSR PST
8. RP  TP
9. MQ  QN
24. BO = 16.9
2. AB = 8
6. a. 8 cm b. circle
reasons
11. a. 8
b. 5
1. Given
2. Radius  chord
12. AB = 12
3. Reflexive
4.  forms rt <
13. a. 15∏ b. 18∏
5.  forms rt <
6. All rt <’s 
7. SAS
8. CPCTC
9.  chords are =dist from center
10.3
1. a. 6 b. 2 c. 5 d. 4 e. 3 f. 7 g. 1
2. a.
b.
c. 180 d. m
e. No the arcs must be in the same circle
or congruent circles
3. a 90 b. 130 c. 230 d. 180 e. 220
4.
9a. 1/45 10a. 216 11. 132
6.
statements
1. Given
2. AB  AC
3.
reasons
1. Given
2. If angles then sides
3.  chords ->  arcs
8.
Statements
1. Given
2.
reasons
1. Given
2.  chords ->  arcs
3.
3. Reflexive
4.
4. Addition
5. BD  AC
5.  arcs ->  chords
Statements
1. Given
2. <ABD <CDB
3. BA  DC
4. BD  BD
5. ABD CDB
6. AD  BC
7. ABCD
reasons
1. Given
2.  arcs -> central angles
3. All radii 
4. Reflexive
5. SAS
6. CPCTC
7. Both pairs of sides 
16.
9d. 7/8
10.4
1. AC = 17cm
3.
2. XY = 12
statements
1. Given
2. PQ  PR
3. Draw RO, OQ
4. RO  OQ
5. PO  PO
6. PRO PQO
7. <QPO <RPO
8. PO bis <RPQ
5. a. Q(16, 0) S(38, 0) b. 3
reasons
1. Given
2. Two-tangent theorem
3. 2 points make a line
4. All radii 
5. Reflexive
6. SSS
7. CPCTC
8. Defn bisector
10b. 200
6. OC = 2.5
9.
Statements
1. Given
2. PW  PZ
3. PX  PY
4. WX  YZ
10. AD = 23
reasons
1. Given
2. Two-tangent theorem
3. Two-tangent theorem
4. Subtraction
16.
Radius of A= 3
Radius of B = 5
Radius of C = 8
Pacing Chart for 10.1-10.4
Date:
Date:
Date:
Date:
10.1-10.4 packet
distributed
10.2 Examples
Q/A 10.2
10.3 Examples
Q/A 10.1
Skill Set 10.1-10.2
Q/A 10.3
10.3 Examples
10.1 Examples
Date:
Date:
Date:
10.4 Examples
Q/A 10.4
Homework 10.1-10.4
Q/A 10.3
Skill Set 10.3-10.4
10.1-10.4 packet due
Quiz 10.1-10.4
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