Pythagorean Theorem and Circles Test A

Find the length of the missing side.

1.

13

12

____ 2. Triangle ABC has side lengths 20, 21, and 29. Do the side lengths form a Pythagorean triple? Explain. A. No, they do not form a Pythagorean triple; . B. Yes, they form a Pythagorean triple; and 20, 21, and 29 are all nonzero whole numbers. C. No, they do not form a Pythagorean triple; although , the side lengths do not meet the other requirements of a Pythagorean triple. D. Yes; they can form a right triangle, so they form a Pythagorean triple.

Find the length of the missing side.

3.

16 m

9 m Not drawn to scale

4. A right triangle has a hypotenuse length of 28, and one side length of 16. Do the side lengths form a

Pythagorean triple? Explain.

5. A triangle has sides that measure 24 cm, 56 cm, and 42 cm. Is it a right triangle? Explain.

____ 6. Circle O and circle P are congruent. What can you conclude from the diagram?

B

P C ) A F

O )

D

E A. COA = DPF C. BOA DPE B. D. none of these

____ 7. and are diameters. Find the measure of .

Y Z

61º X R 47º C

W

A. 72 B. 227 C. 241 D. 288

____ 8. What are the minor arcs of ?

B

A C O

D

A. C. B. D.

____ 9. What are the major arcs of that contain point J?

J

H K O

L

A. B. C. D.

____ 10. Identify a semicircle that contains C.

C

A B 0

A. C. B. D.

____ 11. Name the major arc and find its measure.

A

)50° D C B

A. ; 50 B. ; 50 C. ; 310 D. ; 310



____ 12. Find the measure of .

A E 103° 50° D 27° B O 35°

C

A. 275 B. 75 C. 85 D. 95

13. Grade 7 students were surveyed to determine how many hours a day they spent on various activities. The results are shown in the circle graph below. Find the measure of each central angle in the circle graph. a. homework b. socializing

14. Name the minor arc and find its measure.

A

115° D C )

B

Find the circumference. Leave your answer in terms of .

15.

6.1 cm

____ 16.

12 in.

A. in. B. in. C. in. D. in.

____ 17. Find the length of . Leave your answer in terms of . X

Y 12 m P

A. 6 m B. 1080 m C. 36 m D. 18 m

____ 18. Find the length of arc XY. Round your answer to the nearest tenth. X

Y 6 m P

A. 20.8 m B. 18.8 m C. 28.3 m D. 16.8 m

Find the area of the circle. Leave your answer in terms of .

19.

1.2 m

____ 20.

8.6 m

A. 18.49 m2 B. 36.98 m2 C. 20.2 m2 D. 73.96 m2

____ 21. Find the area of the figure to the nearest tenth.

A. 70.5 in.2 B. 50.7 in.2 C. 77.5 in.2 D. 20.1 in.2

____ 22. Find the area of a sector with a central angle of 200° and a diameter of 7.9 cm. Round to the nearest tenth. A. 3.4 cm2 B. 8.8 cm2 C. 108.9 cm2 D. 27.2 cm2

____ 23. Find the area of a sector with a central angle of 180° and a diameter of 5.7 cm. Round to the nearest tenth.

A. 12.8 cm2 B. 2.2 cm2 C. 51 cm2 D. 5.7 cm2

____ 24. The area of sector AOB is . Find the exact area of the shaded region to the nearest tenth.

A

B O 4 ft

A. 20.6 C. -6.4 B. 4.6 D. none of these

25. Find the exact area of the shaded region to the nearest tenth.

A

B O 16 in.