Given: with Given: and Given: in Given:

29. Given: Quadrilateral

ABCD is circumscribed about Prove:

30. Given: in

Prove:

31. Does it follow from Exercise 30

that is also congruent to ? What can you conclude about and in the drawing? What can you conclude about and ?

32. In not shown,

is a diameter and T is the midpoint of semicircle . What is the value of the ratio ? The ratio ?

33. The cylindrical brush

on a vacuum cleaner is powered by an electric motor. In the figure, the drive shaft is at point D. If find the measure of the angle formed by the drive belt at point D; that is, find .

34. The drive mechanism on a treadmill is powered by an

electric motor. In the figure, find if is 36° larger than

35. Given: Tangents , , and to at

points M, N, and P, respectively , , Find: AM, PC, and BN AC = 12 BC = 16 AB = 14 }O AC BC AB mAC ¬. m ABC ២ m ∠D m ∠D mAC ¬ = 160°, RT RO RT RS RTS ២ RS }O EB DE CE AE 䉭CBE 䉭ADE 䉭ABD ⬵ 䉭CDB }P AB ⬵ DC DA + BC AB + CD = }O C A D B E P Exercises 30, 31 C A D B C A D B Exercises 33, 34 C D B A O N M C A B P O B A O D P Exercises 38, 39 Exercises 42, 43

36. Given: is inscribed in

isosceles right The perimeter of is Find: TM 8 + 4 22 䉭RST 䉭RST }Q N M R S P Q T

37. Given: is an external

tangent to and at points A and B ; radii lengths for and are 4 and 9, respectively Find: AB HINT: The line of centers contains point C, the point at which and are tangent.

38. The center of a circle of radius 3 inches is at a distance

of 20 inches from the center of a circle of radius 9 inches. What is the exact length of common internal tangent HINT: Use similar triangles to find OD and DP. Then apply the Pythagorean Theorem twice. AB ? }Q }O OQ }Q }O }Q }O AB B A O Q C

39. The center of a circle of radius 2 inches is at a distance

of 10 inches from the center of a circle of radius length 3 inches. To the nearest tenth of an inch, what is the approximate length of a common internal tangent? Use the hint provided in Exercise 38.

40. Circles O, P, and Q are

tangent as shown at points X, Y, and Z. Being as specific as possible, explain what type of triangle is if: a , , b , ,

41. Circles O, P, and Q are tangent as shown at points X, Y,

and Z. Being as specific as possible, explain what type of triangle is if: a , , b , ,

42. If the larger gear has 30 teeth and the smaller gear has

18, then the gear ratio larger to smaller is 5:3. When the larger gear rotates through an angle of 60°, through what angle measure does the smaller gear rotate? QZ = 2 PY = 2 OX = 2 QZ = 1 PY = 4 OX = 3 䉭PQO QZ = 2 PY = 3 OX = 2 QZ = 1 PY = 3 OX = 2 䉭PQO O Q P X Y Z Exercises 40, 41