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HonorsGeometry Chapter10ReviewQuestionAnswers
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1.
2.
m∠B = 12 80 - x( )
⇒ 30 = 80 - x
⇒ x = 50°
m∠B = 12 30( ) = 15°
Find the value of x mHG( )
x°
80°
30°
G
H E
F
A
C
B
120°
m∠Y = 12 120 - 56( ) = 32°
m∠AXB = 12 120 + 56( ) = 88°
Find m∠AXB and m∠Y
56°X Y
A
B
D
C
HonorsGeometry Chapter10ReviewQuestionAnswers
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3.
4.
200 = 2y
⇒ y = 100
⇒ x = 40
y x70° 30°30 =
12
y - x( ) ⇒ 60 = y - x
70 = 12
y + x( ) ⇒ 140 = y + x
Find mPQ
XY
A
B
P
Q
x + 8
7
⇒ r = 25cm 7, 24, 25 ( )
16x = 112
⇒ x = 7
- x2 + 576 = r2
x2 + 16x + 464 = r2
24( )2 + x2 = r2
⇒ x2 + 576 = r2
20( )2 + x + 8( )2 = r2
⇒ 400 + x2 + 16x + 64 = r2
⇒ x2 + 16x + 464 = r2
20
24
r
r
48
40
Find the radius of a circle in which a 48 cm. chord is 8 cm closer to the center than a 40 cm chord.
O
HonorsGeometry Chapter10ReviewQuestionAnswers
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5
6
d = 32 + 45 = 77 cm4532
d
7568
120
Two circles intersect and have a common chord that measures 120 cm. The radii of the circlesare 68 cm and 75 cm. Find the distance between their centers.
112°
25°
56°
12 87 + mAB( ) = 56
⇒ mAB = 112 - 87 = 25°
m∠SXY = 12 112( ) = 56°
Find mAB
87°
Y
SX
A
B
D
C
HonorsGeometry Chapter10ReviewQuestionAnswers
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7.
8
3915
3636
Find the radius of a circle if a 72-cm chord is 15 cm from the center.
x - 2
x + x - 2( ) = 8
⇒ 2x = 10
⇒ x = 5
x - 2 13 - x
13 - x
x
x
Find AB
8
13
11
B
A
HonorsGeometry Chapter10ReviewQuestionAnswers
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9.
10.
⇒ mBDE = m∠BOE = 3 45( ) = 135°
m∠BOC = 3608 = 45°
If ABCDEFGH is regular, find the measure of BDE
H
D
F
B
E
G
C
O
A
3
12
12
13
5
3
2 38
Given O with radius 8, P with radius 3, and OP = 13, find the length of the common externaltangent.
PO
HonorsGeometry Chapter10ReviewQuestionAnswers
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11.
12.
12
8
12
8
Two circles with radii 8 cm and 12 cm are 5 cm apart. Find the length of the common internal tangent.
The internal tangent is 15 the same as the third side of the red , which is a 15-20-25 right ( )
15
8
5
12
∴ Radius of A = 3
Radius of B = 8 - 3( ) = 5
Radius of C = 11 - 3( ) = 8
8 - x( ) + 11 - x( ) = 13
⇒ 19 - 2x = 13
⇒ 6 = 2x
⇒ x = 3
8 - x
8 - x
11 - x
11 - x
x
x
8
13
11
A, B, and C are all tangent to each other. AB = 8, BC = 13, and AC = 11. Find the radii of the three s.
A
B
C
HonorsGeometry Chapter10ReviewQuestionAnswers
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13.
14.
3
3
60°30°
Total length of cable = 2! + 6 3( ) "16.68 ft.
Length of CE = 120360
2! 3( )( ) = 2!120°
3 33 3
6 ft.
A flatbed truck is hauling a cylindrical container with a diameter of 6 ft. Find, to the nearesthundredth, the length of a cable needed to hold down the container.
EC
F
DA B
25
25
BP = 25 a side of a square( )
Since we have a square, the diagonal is 25 2. The radius is 25, so PA = 25 2 - 25 cm.
25
A circular garbage can is wedged into a rectangular corner. The can has a diameter of 50 cm.
a. Find the distance from the corner point to the point of contact of the can with the wall PB( )
b. Find the distance from the corner point to the can PA( )
A
PB
HonorsGeometry Chapter10ReviewQuestionAnswers
Baroody Page8of15
15.
16.
23
23
BP = 23 3 longer side of 30-60-90 ( )
Since we have a kite which is split into two30-60-90 s, the diagonal is 46. The radius is23, so PA = 46 - 23 = 23 cm.
30°30°
A circular garbage can is wedged into a corner angled at 60°. The can has a diameter of 46 cm.
a. Find the distance from the corner point to the point of contact of the can with the wall PB( )
b. Find the distance from the corner point to the point on the can that is closest to it PA( )
AP
C
O
B
286°
∴ m∠A = 12
286 - 74( ) = 106°
74°
x + 4x - 10( ) = 360
⇒ 5x = 370
⇒ x = 74°
⇒ 4 74( ) - 10( ) = 286°
Find the measure of a tangent-tangent angle if the measure of the major intercepted arc is 10 lessthan 4 times the measure of the minor intercepted arc.
A
HonorsGeometry Chapter10ReviewQuestionAnswers
Baroody Page9of15
17.
18.
19.
m∠A = 12
30 + 120( ) = 75°
m∠B = 12
120 + 150( ) = 135°
m∠C = 12
150 + 60( ) = 105°
m∠D = 12
60 + 30( ) = 45°
120°
150°
60°
30° x + 2x + 5x + 4x = 360
⇒ 12x = 360
⇒ x = 30°
A quadrilateral is inscribed in a circle. Its vertices divide the circle into four arcs in the ratio 1:2:5:4. Find the measures of the angles of the quadrilateral.
D
A
B C
x x
152 = 5 5 + 2x( )
⇒ 225 = 25 + 10x
⇒ 10x = 200
⇒ x = 20
5
15
TP is a tangent segment. Find the radius of O.
PO Q
T
17 = 85360
2!r( )
⇒ 72 = 2!r
⇒ 36! = r
17 85°
Find the radius of a circle if a central angle of 85° intercepts an arc with length of 17 feet.
HonorsGeometry Chapter10ReviewQuestionAnswers
Baroody Page10of15
20.
21.
92 = 3x
⇒ 81 = 3x
⇒ x = 27
⇒ Diameter = 30
⇒ Radius = 15
x
3
9
9
Given the information shown below, find the radius of the arc.
a = 50°b = 20°c = 15°d = 130°e = 130°f = 25°g = 25°h = 45°i = 70°j = 35°k = 90°m = 35°
JB is a tangent to P. Find the measure of all the letters angles and arcs.
m
k
j
hg
f
d
ci
e
b
a
90°
10°50°
P
J
B
HonorsGeometry Chapter10ReviewQuestionAnswers
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22.
23.
∴ mDC = 2 4x - 15( )°( ) = 2 76 - 15( ) = 2 61( ) = 122°
x + 7( )° = 3x - 31( )°
⇒ x = 19
M is the midpoint of BA. Find mDC.
x + 7( )°
3x - 31( )°
4x - 15( )°
A
M
D
C
B
m∠P = 12 162 - 104( ) = 29°
m∠STQ = 12 162( ) = 81°
90°
mRQ = m RT - m QT = 176° - 104° = 72°
⇒ mRS = 90°
72°
94°
104°
88°
QP is a tangent. Find m∠P and m∠STQ.
R
PQ
T
S
HonorsGeometry Chapter10ReviewQuestionAnswers
Baroody Page12of15
24.
25.
62 = 132
+ x( ) 132
- x( )⇒ 36 =
1694
- x2
⇒ x = ± 254
= 5213
2 - x
∴ RB = 132
- 52
= 4
132
x
13
6
AB is a diameter of P. RQ ⊥ AB, AB = 13, and QR = 6. Find RB.
Q
RB
PA
∴ mPQ = 180° - 43° = 137°
43°
m∠YRX = 12
· m WZ – m YX( ) = 12
126° - 40°( ) = 43°
PZ and QW are tangents to the smaller circle. mWZ = 126° and mYX = 40°. Find mPQ.
P
R
X
Z
W
YQ
HonorsGeometry Chapter10ReviewQuestionAnswers
Baroody Page13of15
26.
27.
P = 212
4π( )( ) + 212
9π( )( ) = 13π
4
9
Find the outer perimeter of the figure, which is composed of semicircles mounted on the sides of arectangle.
3
P = 2 3( ) + 12
2π2( ) + 12
2π5( )
= 6 + 2π + 5π = 6 + 7π
3
4
Find the complete perimeter of the figure.
HonorsGeometry Chapter10ReviewQuestionAnswers
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28.
29.(Thisisahardone,butnotallthatlong~7steps)
A
A
5. CT ≅ DT 5. Definition of midpoint of an arc
7. CAT ∼ TAB 7. AA ∼ 4, 5( )
Given:
Prove:
OBT tangent at TT is midpoint of CD
CAT ∼ TAB
Statements Reasons
6.
4.3.2.
1. Given
A radius to a point of tangency is ⊥ to the tangentAn ∠ inscribed in a semicircle is rightAll right ∠s are ≅
∠s inscribed in ≅ arcs are ≅6. ∠CAT ≅ ∠TAB
3. ∠ACT is right4. ∠ATB ≅ ∠ACT
2. ∠ATB is right
1. O BT tangent at T T is midpoint of CD
D
BT
O
A
C
5. ∠BAT ≅ ∠DCT
7. AC:CT = BD:DT6. AB CD
3. mDT = mBT
4. Draw AB & CD
2. Draw tangent line TS
1. P & Q are internally tangent at T.
5. ∠s inscribed in arcs of the same measure arecongruent
7. Side-Splitter Theorem6.
4.
3.
2.
1. Given
Auxiliary Lines
Arcs inscribed in the same tangent-chord( )∠ have the same measure
Auxiliary Lines
CAP
Given:
Prove:
P & Q are internallytangent at T.
AC:CT = BD:DT
Statements Reasons
D
C
PA
Q
T
B
S
HonorsGeometry Chapter10ReviewQuestionAnswers
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30.
Means-Extremes Products Theorem7.7. AB( ) BC( ) = DB( ) BE( )
6. ABEB
= DBBC
6. CSSTP
A5. ADB ∼ ECB 5. AA ∼ 3, 4( )
A
Given:
Prove:
AC & DE are chords
AB( ) BC( ) = DB( ) BE( )
Statements Reasons
4.3.2.
1. Given
Auxiliary Lines∠s inscribed in the same arc are ≅∠s inscribed in the same arc are ≅
3. ∠A ≅ ∠E
4. ∠D ≅ ∠C
2. Draw EC & DA
1. AC & DE are chords
BD
C
E
A
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