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• How do I use
knowledge of circles
to find arcs and
1. The circle is circumscribed by the pentagon as shown (not drawn to
scale). If QZ = 10, YX = 9, XW = 13, UW = 16, and SU = 17, find the
perimeter of the pentagon.
2. You are standing at point B. Point B is 20 feet from the center of the
circular water storage tank and 18 feet from point A. AB is tangent to OO
at A. Find the radius of the tank.
3. Given: In OO, m BAC = 306°. Find mA.
4. Give the center and radius of circle A and circle B. Describe the
intersection of the two circles and describe all common tangent.
5. AB is tangent to OO at A (not drawn to scale). Find the length of the
radius r, to the nearest tenth.
6. Use the clock to estimate the minor arc measure formed by the hour
and minute hands at 2:15.
7. Find the measure of DBC in OP.
8. Find the value of x.
9. Given circle O with radius 20 and OC = 12. Find the length of AB.
10. Given: mIED = 103° and mJFG = 97°
Find the measure of each unknown angle. (not drawn to scale)
11. Find mBC and mD.
12. Given: mX = 130; WZ = YZ ; mY = 100°
Refer to the diagram to find the measure of each of the following:
13. Given that DAB and DCB are right angles and mACD =312,
what is the measure of ADB?
14. What must be the measures of B and C so that a circle can be
circumscribed about ABCD?
Use the diagram (not drawn to scale) and the given information.
15. mBCD = 111, mDEF = 100, mFGH = 127, and mHAB = 22
16. A park maintenance person stands 20 m from a circular monument. If
you draw two tangents from the maintenance person to each side of the
monument, they make an angle of 25o. What is the measure of the arc
created where the lines intersect the monument?
Use the diagram (not draw to scale) and the given information.
17. Find the value of x if mAB = 59 and mCD = 47.
18. A hummingbird is flying toward a large tree that has a radius of 7
feet. When it is 34 feet from the center of the tree, its lines of sight form
two tangents. What is the measure of the arc on the tree that the
hummingbird can see?
19. Find the measure of 1.
20. Find the measure of 1.
21. Suppose you stand at a distance from a circular building. Assuming
your lines of sight form tangents to the building and make an angle of
19o, what is the measure of the arc of the building that your lines of sight
22. Write an equation that can be used to find x. Then solve the equation
23. If mG = 25, mH = 20, and mK = 50, what is mGMH? Justify
Use the diagram (not drawn to scale) and the given information to find
the diameter of the circle. Round your answer to the nearest tenth.
24. BC = 13 and DC = 17.
Find the value of x.
Find the value of x.
30. Find the surface area of a sphere that has a diameter of 4 cm. Express
your answer in terms of p.
31. Find the volume of a sphere 14 ft in diameter. Use p = 3.14 and
round your answer to the nearest tenth.
32. Find the diameter of a sphere that has a surface area of 64p in2.
33. If a circle has a diameter of 9 inches, what is the circumference
rounded to the nearest whole number? Use p = 3.14
34. A circle has a circumference of 34 meters. Find its diameter.
35. For a circle of radius 9 feet, find the length of an arc s with a measure
36. A park has a circular swimming pool. The diameter of the pool is
11 m. What is the distance traveled if you swim around the edge of the
pool once? Use p = 3.14
37. Circle O has a radius of 7.39. If mAOB is 112°, then find the length
of AB to one decimal place.
Find the area:
39. The figure below represents the overhead view of a deck surrounding
a hot tub. What is the area of the deck? Use p = 3.14.
40. Find the area of the shaded sector in terms of p.
Trig Word Problems
Word Problem Worksheet