## dietrich_harmon 2 years ago In circle O, CD = 44, OM = 20, ON = 19,CD l OM, EF l ON (The figure is not drawn to scale.)

1. dietrich_harmon

2. dietrich_harmon

a.Find the radius. If your answer is not an integer, express it in radical form. b.Find FN. If your answer is not an integer, express it in radical form. c.Find EF. Express it as a decimal rounded to the nearest tenth.

3. dietrich_harmon

@jim_thompson5910

4. jim_thompson5910

|dw:1360903051401:dw|

5. jim_thompson5910

|dw:1360903107022:dw|

6. dietrich_harmon

i hate geometry..lol

7. jim_thompson5910

|dw:1360903151843:dw| solve for x to find the radius a^2 + b^2 = c^2 20^2 + 22^2 = x^2

8. dietrich_harmon

9. jim_thompson5910

tell me what you get for x

10. dietrich_harmon

42?

11. dietrich_harmon

oops 22

12. jim_thompson5910

20^2 + 22^2 = x^2 400 + 484 = x^2 x^2 = 884 x = ???

13. dietrich_harmon

52

14. dietrich_harmon

i don't know

15. jim_thompson5910

x^2 = 884 x = sqrt(884) x = 2*sqrt(221)

16. jim_thompson5910

17. jim_thompson5910

now you can use this radius to find EF and FN

18. dietrich_harmon

202 + 222

19. jim_thompson5910

solve for y y^2 + 19^2 = (2*sqrt(221))^2 y^2 + 381 = 884 keep going

20. d_loparsaie

What do you do after you solve for y? @jim_thompson5910

21. jim_thompson5910

I let y = EN so to find EF, you need to find 2y this is because EF = 2*EN EF = 2y

22. jim_thompson5910

also, FN = EN, so once you get EN, you have found FN

23. d_loparsaie

y^2 + 361=884?? y^2=523 right?

24. jim_thompson5910

oh somehow I had 381...hmm lol yeah it's 361

25. jim_thompson5910

y^2=523 y=sqrt(523)

26. d_loparsaie

How did you get 884 up there?

27. jim_thompson5910

(2*sqrt(221))^2 = 4*221 = 884

28. d_loparsaie

alright so y=29.73?

29. jim_thompson5910

30. jim_thompson5910

31. d_loparsaie

to leave it in radical form do I just leave it as y=sqrt(523)?

32. jim_thompson5910

yes square roots are considered radicals

33. d_loparsaie

Solving for y solves for both FN and EF..?

34. jim_thompson5910

FN yes since FN = EN

35. jim_thompson5910

but you have to double it to find EF

36. d_loparsaie

So the one we just solved (y) is FN right? and I add FN and EN together.. but how do I do that since its in radical form?

37. jim_thompson5910

or you can double FN to get EF

38. d_loparsaie

1,046? right

39. d_loparsaie

is EF

40. jim_thompson5910

no EF = 2*sqrt(523)

41. d_loparsaie

How do I double Fn to get Ef

42. jim_thompson5910

I just did it

43. d_loparsaie

-___- if 2*sqrt(523) is EF then half of that is Fn and En right..

44. jim_thompson5910

correct

45. d_loparsaie

Alright lol sorry I was confused on which was which. How do I find out what half of the radical is? just divide 523 by 2?

46. jim_thompson5910

it's just 2*sqrt(523) and sqrt(523)

47. d_loparsaie

EF=2*sqrt(523) and EN and FN = sqrt(523) .. wow haha I feel stupid. Thank you so much though!

48. jim_thompson5910

it's fine, yw

49. d_loparsaie

to find 2*sqrt(523) as a decimal rounded to the nearest tenth I multiply 523*2 and then take the square root of that number right?

50. jim_thompson5910

you first take the square root of 523, then you double that result

51. jim_thompson5910

then you round to whatever they want

52. d_loparsaie

so the answer would be 45.74?

53. jim_thompson5910

yep 2*sqrt(523) = 45.74 roughly

54. d_loparsaie

Thank you again

55. jim_thompson5910

sure thing