Geometry Semester 2 Final Assignment 2016 It is very important that you review for the Geometry Final. Here are a few pieces of information you want to know. ¾ Your Final is worth 15% of your overall grade ¾ The final covers concepts from the entire semester, they are the following

o Unit 7 – Similarity o Unit 8 – Right Triangles o Unit 9 – Areas and Surface Areas o Unit 10 – Volumes o Unit 11 – Circles o Unit 12 – Probability

¾ The final is 45 multiple choice problems, here are some tips for multiple choice problems o Read the question before you look at the answer o Come up with the answer in your head before looking at the possible answers, this way the

choices given on the test won't throw you off or trick you o Eliminate answers you know aren't right o Read all the choices before choosing your answer o If there is no guessing penalty, always take an educated guess and select an answer

Finals Schedule Monday, June 6th, 2016 1st period EXAM 7:45 - 9:30 2nd period 9:40 -10:19 3rd period 10:24 -11:03 4th period 11:08 -11:47 Lunch 11:47 -12:27 5th period 12:27-1:06 6th period 1:11 -1:50 7th period 1:55 -2:35

Tuesday, June 7th, 2016 2nd period EXAM 7:45 - 9:30 Break 3rd period EXAM 9:40 -11:25 Wednesday, June 8th, 2016 4th period EXAM 7:45 - 9:30 Break 5th period EXAM 9:40- 11:25 Thursday, June 9th , 2016 6th period EXAM 7:45 - 9:30 Break 7th period EXAM 9:40 -11:25

This Assignment is due on the day of your final and is worth 500 assignment points. Make sure you show your work for full credit, circling the correct answer is not enough.

Assigned problems for each day of the Finals Review Date Problems to do that evening

Thursday, May 26 3-9, 11 Friday, May 27 10, 12-19 Tuesday, May 31 20-24, 53 Wednesday, June 1 1, 2, 25-32 Thursday, June 2 33-41, 51, 52, 54, 55, 56 Friday, June 3 42-49

Multiple Choice: Identify the choice that best completes the statement or answers the question. Figures are not necessarily drawn to scale.

1. The ratios of the areas of square A to square B is 1625

. If the area of square B is 100 𝑐𝑚2, what is the length of a side of square A?

A. 4 𝑐𝑚 C. 10 𝑐𝑚

B. 8 𝑐𝑚 D. 64 𝑐𝑚

2. A statue of a Rubik’s Cube is built from a scale model. The scale of the model to the statue is 6 𝑖𝑛𝑐ℎ𝑒𝑠 to 5 𝑓𝑒𝑒𝑡. What is the ratio of the volume of the model to the volume of the actual statue in cubic feet?

A. 1: 1000

B. 1: 10

C. 216: 125

D. 6: 5

3. What is the scale factor of the dilation of ∆𝐴𝐵𝐶 to image ∆𝐴′𝐵′𝐶′ ?

A. −2

B. 1

C. 2

D. 3

¥ ¥25×=160¥as

ft ×= 64

:o = § 5×12=60 in

to .

it-2,1 )

A '

tb ,3)

4. Apply the dilation 𝐷: (𝑥, 𝑦) → (4𝑥, 4𝑦) to the polygon with the given vertices. Name the coordinates of the image points.

A. 𝐴′(8, 4), 𝐵′(16, 4), 𝐶′(16, −12)

B. 𝐴′(8, 4), 𝐵′(16, 4), 𝐶′(16, 12)

C. 𝐴′(0.5, 0.25), 𝐵′(1, 0.25), 𝐶′(1, −0.75)

D. 𝐴′(0.5, 0.25), 𝐵′(1, 0.25), 𝐶′(1, 0.75)

5. What is the value for 𝑥 ?

A. 𝑥 = 18

B. 𝑥 = 16

C. 𝑥 = 12

D. 𝑥 = 3

6. In the figure below, what is the length of 𝐴𝐵̅̅ ̅̅ ?

A. 𝐴𝐵 = 7

B. 𝐴𝐵 = 11

C. 𝐴𝐵 = 16

D. 𝐴𝐵 = 20

A 12,1)

A 'l8 , 9)

BC 4,1 )B

'

(16,4×3+-12)

×a=E ¥I±*

:÷ :E

16×-32=5×+954*7-8 -

5×+32-5×+32

287 T¥ n20

7. Two triangles are similar and the ratio of each pair of corresponding sides is 2: 1 . Which statement regarding the two triangles is not true?

A. Their perimeters have a ratio of 2: 1

B. The scale factor is a ratio of 2: 1

C. Their corresponding angles have a ratio of 2: 1

D. Their areas have a ratio of 4: 1

8. What is the value of 𝑛 ?

A. 𝑛 = 39

B. 𝑛 = 54

C. 𝑛 = 63

D. 𝑛 = 90

9. In ∆𝐿𝑀𝑁, 𝑆 is the midpoint of 𝐿𝑀̅̅ ̅̅ , 𝑇 is the midpoint of 𝑀𝑁̅̅ ̅̅ ̅, and R is the midpoint of 𝐿𝑁̅̅ ̅̅ . Given the following, what is the perimeter of ∆𝑅𝑆𝑇 ?

x 𝐿𝑆 = 8.2𝑥 x 𝑆𝑇 = 4.3𝑥 x 𝑀𝑁 = 6𝑥

A. 11.4𝑥

B. 15.5𝑥

C. 18.4𝑥

D. 18.5𝑥

30

:- 3¥ ⇒F

3h :*. =

:8.2×3×9.3×8.ttzx 8.2 ''

zx /4.3×4.3 ×

3×+8.2×+4.3×15.5x

10. Use the diagram to find the values of x and y.

A. 𝑥 = 5√15, 𝑦 = 20√5

B. 𝑥 = 5√15, 𝑦 = 10√5 C. 𝑥 = 5√5, 𝑦 = 20√5 D. 𝑥 = 5√5, 𝑦 = 10√5

11. Three students were asked to explain which transformations map the pre-image of ∆𝑋𝑌𝑍 onto the image ∆𝑋′𝑌′𝑍 in the diagram below.

Based on the following responses, whose reasoning is correct? x Jason says the image is result of translating the pre-image along the vector ⟨1, −2⟩

and performing a dilation with a scale factor of 3.

x Sanjay says the pre-image is rotated 180° about the origin and dilated by a scale factor of 3.

x Teresa says the image is a result of applying the rule (𝑥, 𝑦) → (3(𝑥 + 1), 3(𝑦 − 2)). A. Jason and Teresa are correct.

B. Sanjay and Jason are correct.

C. Only Jason is correct.

D. Jason, Sanjay, and Teresa are all correct.

: ×=2¥stroke-

108:¥ 12

,- 3)

YEY ,3)

4 't -9,3 )p . $

zt2 ,2¥3,0 )

.

12. In the right triangle, 𝑥 and 𝑦 represent unknown side lengths. What is the length of side 𝑥 ?

A. 2

B. 4

C. 2√3 D. 3√2

13. In the figure, what is the distance a ball travels when thrown from second base to home plate?

A. 90 𝑓𝑒𝑒𝑡

B. 180 𝑓𝑒𝑒𝑡

C. 90√2 𝑓𝑒𝑒𝑡

D. 2√90 𝑓𝑒𝑒𝑡

14. What is cos 𝑥° in the triangle?

A. 40

41 C. 41

9

B. 941

D. 940

:3

X=2 . 2=4

y

.=2:= 902+90

'

×=9::

±

% S × = 4041

15. Which of the following has the same value as sin 𝑀 ? A. sin 𝑁

B. tan 𝑀

C. cos 𝑁

D. cos 𝑀

16. What is the measure of angle A in the triangle, rounded to the nearest degree?

A. 35°

B. 44°

C. 46°

D. 72°

17. A person is standing at ground level with the base of the Empire State Building in New York City. The angle formed by the ground and a line segment from his position to the top of the building is 48.4°. The height of the Empire State Building is 1472 feet. Find the distance that he is standing from the base of the Empire State Building to the nearest foot.

A. 8 𝑓𝑒𝑒𝑡 C. 1968 𝑓𝑒𝑒𝑡

B. 1307 𝑓𝑒𝑒𝑡 D. 2217 𝑓𝑒𝑒𝑡

Set CITE= MP

ntn ^a

0o

m

m/p a

YpA n Cr:

cos A.A = cos

' ' 740a

*÷p€en#tIIII?

18. Find the value of x in the diagram below. Round your answers to the nearest tenth if necessary.

A. 𝑥 = 12.2

B. 𝑥 = 13.1

C. 𝑥 = 24.5

D. 𝑥 = 26.2

19. Three students were asked to find the value of x in the diagram below.

The first step of each student’s work is shown below. Determine which student(s) set up the problem correctly.

Lewis Alexa Miranda

cos 26 =𝑥

16 tan 26 =

7𝑥

sin 64 =16𝑥

A. Lewis, Alexa, and Miranda

B. Miranda and Alexa C. Lewis and Miranda D. Lewis and Alexa

20. In a large city, a circle with a radius of 3 𝑚𝑖𝑙𝑒𝑠 contains a population of 30,348 people. What is the expected population of a circle with a 4 𝑚𝑖𝑙𝑒 radius in the same city?

A. 121,392 𝑝𝑒𝑜𝑝𝑙𝑒 C. 53,952 𝑝𝑒𝑜𝑝𝑙𝑒

B. 91,044 𝑝𝑒𝑜𝑝𝑙𝑒 D. 40,464 𝑝𝑒𝑜𝑝𝑙𝑒

.

y2+H±2l?

n T y=8Bo

a

sin 43=8£

×=8t⇐ 42

o

a

h÷

: =4

r :3 miles A=t92

A= -11.32 3013481073.4×16 'T

30,348 53952#g= 1073.41mi -

21. What is the area of a regular hexagon with an apothem of 10 𝑐𝑚 and a side length of 20√3

3 𝑐𝑚 ?

A. 200√3 𝑐𝑚2

B. 300√3 𝑐𝑚2

C. 600√3 𝑐𝑚2

D. 600 𝑐𝑚2

22. Given that the side of the regular pentagon is 8 𝑓𝑡, what is the approximate area of the shaded triangle?

A. 11 𝑓𝑡2

B. 22 𝑓𝑡2

C. 8√3 𝑓𝑡2

D. 16√3 𝑓𝑡2

23. What best describes the cross section shown on the cube?

A. square C. trapezoid

B. triangle D. rectangle

A--

'

be

¥205×6=400

A = Ya . 10.4035

A = 2005cm

: an 36=1#f. *⇐

8 € Fitits .

8.5.548

" 22 .

0

-

24. A layered cake is a solid of revolution. Which of the following is the drawing of a two-dimensional shape and an axis of rotation that could form the cake?

A.

C.

B.

D.

25. Jamal wants to fill a container with two different colors of sand for an art project. The

container is 9 𝑖𝑛𝑐ℎ𝑒𝑠 tall and has a regular polygon base. He is going to fill part of the container with 10 𝑖𝑛3 of blue sand. How much green sand does Jamal need to purchase to fill the rest of the container? Round your answer to the nearest tenth if necessary.

A. 36.8 𝑖𝑛3

B. 44 𝑖𝑛3

C. 46.8 𝑖𝑛3

D. 54 𝑖𝑛3

:- BBH - 10

B=9+9

f- t.gr -9 - 10

V :

46.8¥o

#jxttI5A=' 12.6.30

A=9J

26. Compare the volumes of the cone and the regular pyramid below. Which statement is true?

ℎ𝑒𝑖𝑔ℎ𝑡 12 𝑖𝑛𝑐ℎ𝑒𝑠 𝑟𝑎𝑑𝑖𝑢𝑠 7 𝑖𝑛𝑐ℎ𝑒𝑠

ℎ𝑒𝑖𝑔ℎ𝑡 7 𝑖𝑛𝑐ℎ𝑒𝑠

𝑠𝑖𝑑𝑒 𝑙𝑒𝑛𝑔𝑡ℎ 12 𝑖𝑛𝑐ℎ𝑒𝑠

A. The volume of the pyramid is about 140 𝑖𝑛3 more than the volume of the cone.

B. The volume of the cone is about 279.8 𝑖𝑛3 more than the volume of the pyramid.

C. The volume of the cone is about 531.8 𝑖𝑛3 more than the volume of the pyramid.

D. The volume of the cone is about 112 𝑖𝑛3 more than the volume of the pyramid.

27. A tanker truck can carry 3,000 𝑔𝑎𝑙𝑙𝑜𝑛𝑠 of fuel and is going to fill an empty cylindrical gas tank with a height of 4 𝑓𝑒𝑒𝑡. The operator doesn’t know the radius of the tank and is unsure whether the tank will be able to hold all of the fuel. When the height of the fuel in the tank reaches 1 𝑓𝑜𝑜𝑡, the operator looks at the pumping gauge and determines that approximately 846 𝑔𝑎𝑙𝑙𝑜𝑛𝑠 of fuel were pumped into the tank. Based on this information, will the tank hold all 3,000 𝑔𝑎𝑙𝑙𝑜𝑛𝑠 of fuel? Explain.

A. Yes, the tank can hold a total of 4,280 𝑔𝑎𝑙𝑙𝑜𝑛𝑠 of fuel.

B. Yes, the tank can hold a total of 3,384 𝑔𝑎𝑙𝑙𝑜𝑛𝑠 of fuel.

C. No, the tank can only hold a total of 2,538 𝑔𝑎𝑙𝑙𝑜𝑛𝑠 of fuel.

D. No, the tank can only hold a total of 2,154 𝑔𝑎𝑙𝑙𝑜𝑛𝑠 of fuel.

Viblr?h Vi 'lsBhB= 12×12=144

Va 'btt?l2 h=7

1961T f- 113.1447615.8

V=3:

46×4

3384

28. Three students were asked to find the volume of a cylinder with a hemisphere removed from one end.

Each student’s work is shown below. Determine which student is correct.

Student X Student Y Student Z

𝑉𝑜𝑙𝑢𝑚𝑒 = 𝜋𝑟2ℎ −12

(43

𝜋𝑟3)

= 𝜋 ∙ 52 ∙ 6 −12

(43

𝜋 ∙ 53)

= 150𝜋 −12

(500

3𝜋)

= 150𝜋 −250

3𝜋

=200

3𝜋 𝑖𝑛3

𝑉𝑜𝑙𝑢𝑚𝑒 = 𝜋𝑟2ℎ −43

𝜋𝑟3

= 𝜋 ∙ 32 ∙ 10 −43

𝜋 ∙ 33

= 90𝜋 − 36𝜋

= 54𝜋 𝑖𝑛3

𝑉𝑜𝑙𝑢𝑚𝑒 = 𝜋𝑟2ℎ −12

(43

𝜋𝑟3)

= 𝜋 ∙ 32 ∙ 10 −12

(43

𝜋 ∙ 33)

= 90𝜋 −12

(36𝜋)

= 90𝜋 − 18𝜋

= 72𝜋 𝑖𝑛3

A. Student X is correct.

B. Student Y is correct. C. Student Z is correct. D. None of the students is correct.

29. What is the height of a square pyramid that has a side length of 13 𝑓𝑒𝑒𝑡 and a volume of 1521 𝑓𝑡3 ?

A. ℎ = 3 𝑓𝑒𝑒𝑡 C. ℎ = 27 𝑓𝑒𝑒𝑡

B. ℎ = 9 𝑓𝑒𝑒𝑡 D. ℎ = 39 𝑓𝑒𝑒𝑡

o o

:YZBH

B= 13.13=169

V= 1521

1521 = Yz . 169 - h

h=27

30. A food manufacturer sells yogurt in cone shaped cups with the dimensions shown. To the nearest tenth, how many fluid ounces of yogurt does the cup hold if 1 𝑐𝑚3 ≈ 0.034 𝑓𝑙 𝑜𝑧 ?

A. 0.6 𝑓𝑙 𝑜𝑧

B. 5.7 𝑓𝑙 𝑜𝑧

C. 17.1 𝑓𝑙 𝑜𝑧

D. 22.8 𝑓𝑙 𝑜𝑧

31. What is the volume of the sphere in terms of 𝑥 ?

A. 36𝜋𝑥3 𝑓𝑡3

B. 48𝜋𝑥3 𝑓𝑡3

C. 288𝜋𝑥3 𝑓𝑡3

D. 864𝜋𝑥3 𝑓𝑡3

32. You want to design a cylindrical container for oatmeal that has a volume of 90 𝑖𝑛3. You also want the height of the container to be 3.5 times the radius. To the nearest tenth, what should the approximate radius of the container be?

A. 2.0 𝑖𝑛 C. 3.0 𝑖𝑛

B. 2.9 𝑖𝑛 D. 3.1 𝑖𝑛

a Yzrlerhh

ran:

- Yz .li . 42,10

Vie 16¥ 'T× 0.034

v= 5.7

V= 1¥= of .H( 6×73

V=288x

't* = Kph

| / 3°5×go = t.in } .5X

�1�90=7511×3¥19=3#

Xi

2.0

33. Given mAC = mBC and ∠𝐴𝐷𝐵 is a central angle, what is the value of 𝑥 and BC ?

A. 𝑥 = 18, mBC = 136°

B. 𝑥 = 9.2, mBC = 88°

C. 𝑥 = 18, mBC = 88°

D. 𝑥 = 9.2, mBC = 136°

34. In the figure below, ∠𝑄𝑃𝑅 is a circumscribed angle. Find the value of x.

A. 𝑥 = 3.5

B. 𝑥 = 5

C. 𝑥 = 8.5

D. 𝑥 = 12

35. What is the measure of RS ? A. 54°

B. 38°

C. 32°

D. 27°

D8 zbo

-88=2722

mBT= 136

- 5×-2=88Sx :

=l8.

\

.

360-255

105 15*255-105

=

:- 5

×

54=11+762

108=11+76

×= 32

36. What is the measure of the inscribed angle (𝑥), if the ray is tangent to the circle?

A. 140°

B. 110°

C. 70°

D. 55°

37. What is the length of the minor arc AB in the circle with a radius of 45 𝑐𝑚 ?

A. 20𝜋 𝑐𝑚

B. 10𝜋 𝑐𝑚

C. 5𝜋 𝑐𝑚

D. 2𝜋 𝑐𝑚

38. What is the area of a circular pool that has a circumference of 100𝜋 𝑓𝑒𝑒𝑡 ?

A. 10𝜋 𝑓𝑡2 C. 100𝜋 𝑓𝑡2

B. 50𝜋 𝑓𝑡2 D. 2500𝜋 𝑓𝑡2

39. The diameter of a circular pizza pan is 18 𝑖𝑛𝑐ℎ𝑒𝑠. Two-thirds of the pizza is eaten by your friends. What is the approximate area of the pizza pan that is covered by the remaining pizza?

A. 170 𝑖𝑛2 C. 54 𝑖𝑛2

B. 85 𝑖𝑛2 D. 27 𝑖𝑛2

10

1¥ ⇒o

×=180¥10

¥0.2 tr

%0.2

't=2kr

10071=2 tr

r= 50

A = IT . 502

At

2501=-18

r=9

st .#:n71T

84.8

40. A circle has an arc length of 10 𝑓𝑒𝑒𝑡. The central angle formed is 60°. What is the area of the sector? (Hint: find the radius first)

A. 150

𝜋 𝑓𝑡2 C.

𝜋360

𝑓𝑡2

B. 𝜋

150 𝑓𝑡2 D.

900𝜋

𝑓𝑡2

41. A large circular cake is cut into the pieces shown below. If a person asks for a smaller piece of cake, which piece of cake should you serve them? Explain.

A. You should serve them piece A because it has an area 0.5𝜋 𝑖𝑛2 less than piece B.

B. You should serve them piece A because it has an area 3.5𝜋 𝑖𝑛2 less than piece B.

C. You should serve them piece B because it has an area 1.75𝜋 𝑖𝑛2 less than piece A.

D. You should serve them piece B because it has an area 8𝜋 𝑖𝑛2 less than piece A.

42. Given the square inside the circle with radius 6. What is the probability that the point lies inside the square, if a point is chosen at random inside the circle?

A.

72 − 36𝜋𝜋

C. √2𝜋

B. 2 − 𝜋

𝜋 D.

2𝜋

to =÷o st÷o#c¥I

10 = Ft r

150r=

3*1 TT

g- .

A . 6'

= Is H -7 14 .1 → B

£ ( to . T.to'

- of TD = 4 t → 12.6 → A

0.5 IT

: :R

6 G . 652= 2

* 2

TT

43. A grab bag contains 7 football cards and 3 basketball cards. An experiment consists of taking one card out of the bag, then selecting another card. What is the probability of selecting a football card, replacing it, and then selecting a basketball card? If necessary, round answers to the nearest hundredth.

A. 0.23 C. 0.21

B. 0.09 D. 0.49

44. A bag contains hair ribbons for a spirit rally. The bag contains 5 black ribbons and 7 green ribbons. Lila selects a ribbon at random, then Jessica selects a ribbon at random from the remaining ribbons. Find the probability that both events 𝐴 and 𝐵 occur. Which is the correct answer in simplest fraction form?

𝐸𝑣𝑒𝑛𝑡 𝐴: 𝐿𝑖𝑙𝑎 𝑠𝑒𝑙𝑒𝑐𝑡𝑠 𝑎 𝑏𝑙𝑎𝑐𝑘 𝑟𝑖𝑏𝑏𝑜𝑛. 𝐸𝑣𝑒𝑛𝑡 𝐵: 𝐽𝑒𝑠𝑠𝑖𝑐𝑎 𝑠𝑒𝑙𝑒𝑐𝑡𝑠 𝑎 𝑔𝑟𝑒𝑒𝑛 𝑟𝑖𝑏𝑏𝑜𝑛.

A.

733

C. 35132

B. 35144

D. 522

45. The table shows the distribution of male and female students and left- and right-handed students in the math club. Find the probability that a female student selected at random is left-handed. Which is the correct answer as a fraction in simplest form?

Left-handed Right-handed Male 2 35

Female 6 36

A. 3

4 C. 1

6

B. 17

D. 679

÷ .

tieit

=¥:4¥

46. The table shows the distribution of the labor force in the United States in the year 2000. Suppose that a worker is selected at random. Find the probability of randomly selecting a worker in the Industry field given that the worker is female. Which is the correct answer as a decimal rounded to the nearest thousandth?

Agriculture Industry Services Male 3,132,000 25,056,000 50,112,000

Female 667,000 8,004,000 57,362,000

A. 0.141 C. 0.121

B. 0.242 D. 0.312

47. Events 𝐴 and 𝐵 are independent. Find the missing probability. 𝑃(𝐴) =_______ 𝑃(𝐵) = 0.3 𝑃(𝐴 𝑎𝑛𝑑 𝐵) = 0.06

A. 0.7 C. 0.2

B. 0.24 D. 0.3

48. If 𝑃(𝐴) = 0.43 and 𝑃(𝐵|𝐴) = 0.89, find 𝑃(𝐴 𝑎𝑛𝑑 𝐵).

A. 0.51 C. 0.11

B. 0.48 D. 0.38

49. The sections on a spinner are numbered from 1 through 8. If the probability of landing on a given section is the same for all the sections, what is the probability of spinning a number less than 4 or greater than 7 in a single spin?

A. 1

2 C. 3

8

B. 18

D. 58

8004000

← 33000

0.06=11. 0.3

X= 0.2

:3×0.89

020,034,547,80¥

50. A certain disease occurs in 4% of the population. A blood test for this disease shows a false positive 12% of the time. That means a test will show positive given that the person does not have the disease. What is the probability that a person tests positive but does not have the disease?

A. 0.12 C. 0.1152

B. 0.125 D. 0.0048

51. If constructing a circumscribed circle, which of the following intersect at a common point?

A. angle bisectors

B. perpendicular bisectors

C. medians

D. midpoints

52. When constructing an inscribed polygon, which of the following tools should be used to place the vertices of the polygon on the circle?

A. a string

B. protractor

C. compass

D. none of the above

0.96×0.12

53. Find the angle measures of 𝐴𝐵𝐶𝐷.

A. 𝑚∠𝐴 = 71° 𝑚∠𝐵 = 54° 𝑚∠𝐶 = 109° 𝑚∠𝐷 = 126°

C. 𝑚∠𝐴 = 35° 𝑚∠𝐵 = 134° 𝑚∠𝐶 = 145° 𝑚∠𝐷 = 54°

B. 𝑚∠𝐴 = 34° 𝑚∠𝐵 = 54° 𝑚∠𝐶 = 146° 𝑚∠𝐷 = 126°

D. 𝑚∠𝐴 = 71° 𝑚∠𝐵 = 50° 𝑚∠𝐶 = 109° 𝑚∠𝐷 = 130°

54. Which circle is inscribed in the triangle?

A. Circle 𝑋

B. Circle 𝑌

C. Circle 𝑍

D. All of the above

3×+7+2×+3=1805×+10=180

5×*-34

3.34+7 180 . log 4.39-10109 71 126

55. The diagram below shows the construction of the center of the circle circumscribed about ∆𝐴𝐵𝐶. Which construction does this figure represent?

A. The intersection of the angle bisectors of ∆𝐴𝐵𝐶

B. The intersection of the medians of ∆𝐴𝐵𝐶

C. The intersection of the altitudes of ∆𝐴𝐵𝐶

D. The intersection of the perpendicular bisectors of ∆𝐴𝐵𝐶

56. Which geometric principle is used in the construction shown below?

A. The intersection of the angle bisectors of a triangle is the center of the inscribed circle.

B. The intersection of the angle bisectors of a triangle is the center of the circumscribed circle.

C. The intersection of the medians of a triangle is the center of the inscribed circle.

D. The intersection of the medians of a triangle is the center of the circumscribed circle.