## Emily778 2 years ago Find the value of x. FG perpendicular to OP, RS perpendicular to OQ, FG=20, RS=24, OP=14

1. Emily778

2. Emily778

@Hunus @jim_thompson5910

3. jim_thompson5910

let r = radius of the circle

4. jim_thompson5910

by the pythagorean theorem, we can say (FP)^2 + (OP)^2 = (OF)^2 10^2 + 14^2 = r^2 solve for r and tell me what you get

5. Emily778

100 + 196 = 296^2. Now what?

6. jim_thompson5910

r^2 = 296 so r = ???

7. Emily778

296

8. jim_thompson5910

no

9. jim_thompson5910

r^2 is 296, not r

10. Emily778

87, 616

11. jim_thompson5910

don't square it though

12. jim_thompson5910

how do you undo squaring something

13. Emily778

sqrt?

14. jim_thompson5910

yep

15. Emily778

16.9?

16. jim_thompson5910

you did sqrt(296) right?

17. Emily778

Yea

18. jim_thompson5910

it's close, but not correct

19. jim_thompson5910

sqrt(296) = 17.2046505340852 round to whatever place you need to

20. Emily778

17.2 isn't one of the answers. Only 16.9

21. jim_thompson5910

but remember, we want x, not r

22. jim_thompson5910

we use r to get x

23. Emily778

the possible answers are: 16.9, 14, 12.3, and 12..

24. jim_thompson5910

$\large r = \sqrt{296} \rightarrow r^2 = 296$ $\large (OQ)^2 + (RQ)^2 = (OR)^2$ $\large (OQ)^2 + (RQ)^2 = r^2$ $\large x^2 + 12^2 = 296$ $\large x^2 + 144 = 296$ ... ... ... $\large x = ???$

25. Emily778

152

26. Emily778

12.3

27. jim_thompson5910

$\large x^2 = 152$ so $\large x = ???$

28. jim_thompson5910

good, x is roughly 12.3

29. Emily778

30. jim_thompson5910

what about it? what do you want to find? and what are you given?

31. Emily778

Oh. Lol. Forgot.\ AB is a diameter and AB is perpendicular to CD.

32. jim_thompson5910

alright so that's all the given info?

33. Emily778

I know the angles are all 90 degrees.

34. jim_thompson5910

what do you need to find exactly?

35. Emily778

Find BD for AC= 58 DEGREES

36. jim_thompson5910

AC is a segment, not an angle

37. Emily778

Okay..

38. jim_thompson5910

so is it ACP or ACB that's 58 degrees

39. Emily778

This is exactly what it says. Find m BD for m AC= 58 degrees.

40. jim_thompson5910

oh arc AC, gotcha

41. jim_thompson5910

angle APC = (1/2)*(arc AC + arc BD) 90 = (1/2)*(58 + x) 90*2 = 58 + x 180 = 58 + x solve for x

42. Emily778

122

43. jim_thompson5910

yep