1 / 50

Review Ch. 10

Review Ch. 10. Complete all problems on a separate sheet of paper. Be sure to number each problem. Good Luck!. Problem #1. Find the exact length of arc AB, if circle P has a radius of 18cm. A. P. 100 °. B. Solution to #1. Arc Length = (100/360) * 36 π

camden
Télécharger la présentation

Review Ch. 10

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Review Ch. 10 Complete all problems on a separate sheet of paper. Be sure to number each problem. Good Luck!

  2. Problem #1 Find the exactlength of arc AB, if circle P has a radius of 18cm. A P 100° B

  3. Solution to #1 Arc Length = (100/360) * 36π = (5/18) * 36π = 10π cm.

  4. Problem # 2 Find the diameter of a circle in which a 36 cm chord is 80 cm from the center.

  5. Solution to #2 This is a 9, 40, 41 triangle times 2 so r = 82cm  diameter = 164 cm.

  6. Problem #3 Find the radius of a circle with a circumference of

  7. Solution to #3 Circumference = π * diameter  so the diameter must be 20  so radius = 10.

  8. Problem #4 Find the measure of arc AE. A 200о B x 210о D E C

  9. Solution to #4 *Arc BC = 360 – 210 = 150о *Angle BDC is supp (tangent-tangent) = 30о *So Angle ADE = 30о *So 30 = (1/2)(200 – x) 60 = 200 – x x = 140о

  10. Problem #5 In the circumscribed polygon, find the length of the AB. 15 A 10 B 12

  11. Solution to #5 AB = 15 – (10 – x) + 12 – x = 5 + x + 12 – x = 17

  12. Problem #6 In circle O, AB is a diameter. OA=3x+5 and OB=2(5x-1). Find AB.

  13. Solution to #6 OA and OB are both radii so are equal. 3x + 5 = 2(5x – 1) 3x + 5 = 10x – 2 7 = 7x 1 = x each radius = 8 ; so diameter AB = 16

  14. B C A Problem #7 Solve for x if and if

  15. Solution to #7 Since angle A is inscribed; 2(5x + 6) = 12x – 2 10x + 12 = 12x – 2 14 = 2x x = 7

  16. Problem #8 MATH is inscribed in the circle. Angle M has a measure of 78 degrees. Find the measure of angle T. A M T H

  17. Solution to #8 Opp. Angles of inscribed quadrilaterals are supp. Measure of Angle T = 180 – 78 = 102о

  18. B C A Problem #9 Find the radius of the circle if AB is a diameter, , and BC=20.

  19. Solution to #9 *Measure of Angle B = 120/2 = 60 *Measure of Angle C = 90 *30 – 60 – 90 triangle with x = 20 ; so diameter is 2x = 40 *Radius of AB is 20.

  20. Problem #10 A circle is inscribed in triangle ABC. AB=14, AC=12 and BC=4. Find BD. A B C D

  21. Solution to #10 14 – x + 12 – x = 4 26 – 2x = 4 22 = 2x x = 11 So BD = 14 – x = 3

  22. Problem #11 A circle has a radius of 50. How far from the center is a chord of length 28?

  23. Solution to #11 7, 24, 25 right triangle So x = 2 * 24 = 48

  24. Problem #12 A regular octagon is inscribed in a circle. What is the measure of an arc cut off by a side of the octagon?

  25. Solution to #12 * Regular - so all chords congruent. * Congruent chords = congruent arcs. 360/8 = 45о

  26. Problem #13 Two concentric circles have radii of lengths 16 and 20. Find the length of a chord of the larger circle that is tangent to the smaller circle.

  27. Solution to #13 • 3, 4, 5 right triangle x = 12 so length of the chord is 24.

  28. Problem #14 A 12 by 10 rectangle is inscribed in a circle. Find the radius.

  29. Solution to #14 • 144 + 100 = c2 244 = c2

  30. Problem #15 Two secants drawn to a circle from an external point intercept arcs that are 122° and 68°. Find the measure of the secant-secant angle. 122° 68° P

  31. Solution to #15 • Angle P = (1/2)(122 – 68) = (1/2)(54) = 27о

  32. Problem #16 • Find the circumference of a circle in which an 80 cm chord is 9 cm from the center.

  33. Solution to #16 • 9, 40, 41 right triangle so r = 41 • C = 2π(41) = 82 π cm

  34. Problem #17 A central angle intercepts an arc that is 5/12 of the circle. Find the measure of angle x. x O of circle O

  35. Solution to #17 • If arc is 5/12  central angle is 5/12 of 360 so central angle is 150о • Radii are congruent so isosceles triangle  only 30о left. • Angle x = 30/2 = 15о

  36. Problem #18 If PA and PB are tangent to circle O at A and B, PA=24, and PO=26, find perimeter of quadrilateral PAOB. A O P B

  37. Solution to #18 • OA is perpendicular to PA  5, 12, 13 right triangle. • OA = 10 and PB = 24 • 10 + 10 + 24 + 24 = 68

  38. Problem #19 Find the measure of angle x. x 44° 92°

  39. Solution to #19

  40. Problem #20 What is the length of a chord that cuts off an arc of 120 degrees in a circle with a radius of 8?

  41. Solution to #20

  42. Problem #21 Parallelogram ABCD is inscribed in circle Q, with dimensions of 24 by 10. Find the area of circle Q.

  43. Solution to #21

  44. Problem #22 Circle A has a radius of 5 inches, and circle B has a radius of 20 inches. The centers are 39 inches apart. Find the length of the common external tangent (CD). D C • • • A • B

  45. Solution to #22

  46. Problem #23 Two tangent segments of a circle with a diameter of 50 inches form a 60 degree angle where they meet at P. How far is P from the center of the circle? P 60°

  47. Solution to #23

  48. B D 76° A C Problem #24 AB & AC are tangent to the circle. Find the measure of arc BDC.

  49. Solution to #24

  50. STUDY!!!!!

More Related