## anonymous one year ago fg is perpendicular to op, rs is perpendicular to oq, fg=32, rs=39 and op=14. find the value of x

1. anonymous

|dw:1434347870486:dw|

2. anonymous

a). 19.5 b). 20.8 c). 14 d). 8.5

3. campbell_st

wow that is such a bad drawing |dw:1434347809810:dw| a little circle geometry the perpendicular line from the centre to a chord, bisects the chord...

4. anonymous

o?

5. anonymous

@campbell_st

6. campbell_st

|dw:1434348391396:dw| so find y using pythagoras' theorem... because if OP bisects FG the PF = 16 and you know OP = 14 y will be a radius. then you can use that to draw another radius for the other side

7. campbell_st

|dw:1434348508637:dw| so use pyhtagoras again to find x, knowing that OQ bisects SR hope it helps

8. campbell_st

hope it helps

9. anonymous

10. campbell_st

19.5 is the length of QS

11. campbell_st

|dw:1434348916381:dw|

12. anonymous

x is 14 @campbell_st

13. campbell_st

no x is not 14... use pythagoras to find y \[y^2 = 16^2 + 14^2\] you can leave it as y^2 what do you get... ?

14. anonymous

20.8 @campbell_st

15. campbell_st

well lets just say \[y^2 = 452\]

16. anonymous

yeah ik thats what i got but but not squared its 20.8

17. campbell_st

then looking at finding x, and using pythagoras again you will have \[y^2 = x^2 + 19.5^2\] which can be re-written as \[x^2 = y^2 - 19.5^2\] making the substitution \[x^2 = 452 - 19.5^2\] and from here you should be able to find x

18. anonymous

8.5

19. campbell_st

thats what I got