Find if . Is it possible for

24. Given: Diameter at

D Prove: CD is the geometric mean of AD and DB AB ⬜ CE A B E C D D C 1 x A B Exercises 25, 26 In Exercises 25 and 26, and are tangents.

25. Given:

Prove: m ∠1 = 180° - x m AB ¬ = x CB CA

26. Use the result from Exercise 25 to find if

.

27. An airplane reaches an altitude of 3 mi above the earth.

Assuming a clear day and that a passenger has binoculars, how far can the passenger see? HINT: The radius of the earth is approximately 4000 mi. m AB ¬ = 104° m ∠1 t 3 4,000 1 2 A E F C D B O A B C N O M

28. From the veranda of a beachfront hotel, Manny is

searching the seascape through his binoculars. A ship suddenly appears on the horizon. If Manny is 80 ft above the earth, how far is the ship out at sea? HINT: See Exercise 27 and note that 1 mi = 5280 ft.

29. For the five-pointed star pentagram, inscribed in the

circles, find the measures of and . ∠2 ∠1

30. For the six-pointed star hexagram

inscribed in the circle, find the measures of and .

31. A satellite dish in the shape of a

regular dodecagon 12 sides is nearly “circular.” Find: a b c inscribed angle

32. In the figure shown,

by the reason AA. Name two pairs of congruent angles in these similar triangles.

33. In the figure shown,

by the reason AA. Name two pairs of congruent angles in these similar triangles.

34. On a fitting for a hex wrench, the distance from the center

O to a vertex is 5 mm. The length of radius of the circle is 10 mm. If at F, how long is ? FC OC ⬜ DE OB 䉭RXV 䉭WXS 䉭RST 䉭WVT m ∠ABC m ABC ២ m AB ¬ ∠2 ∠1 1 2 A B C D E F G H I J K L W R T V S 2 1 Exercises 32, 33

35. Given:

is a diameter of M is the midpoint of chord N is the midpoint of chord , Find: The length of diameter AB AN = 2 113 MB = 1 73 CB AC }O AB

36. A surveyor sees a circular

planetarium through a angle. If the surveyor is 45 ft from the door, what is the diameter of the planetarium? 60° 45 ft Door