Honors Geometry Chapter 10 Review Question Answers 10/2016-2017... · Honors Geometry Chapter 10...

HonorsGeometry Chapter10ReviewQuestionAnswers

Baroody Page1of15

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


Baroody Page2of15

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


Baroody Page3of15

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


Baroody Page4of15

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


Baroody Page5of15

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


Baroody Page6of15

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


Baroody Page7of15

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


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


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.


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


Baroody Page11of15

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


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


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.


Baroody Page14of15

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


Baroody Page15of15

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

Honors Geometry Chapter 10 Review Question Answers 10/2016-2017... · Honors Geometry Chapter 10...

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