fg is perpendicular to op, rs is perpendicular to oq, fg=32, rs=39 and op=14. find the value of x

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fg is perpendicular to op, rs is perpendicular to oq, fg=32, rs=39 and op=14. find the value of x

Mathematics
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|dw:1434347870486:dw|
a). 19.5 b). 20.8 c). 14 d). 8.5
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...

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o?
|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
|dw:1434348508637:dw| so use pyhtagoras again to find x, knowing that OQ bisects SR hope it helps
hope it helps
is the answer 19.5? @campbell_st
19.5 is the length of QS
|dw:1434348916381:dw|
x is 14 @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... ?
well lets just say \[y^2 = 452\]
yeah ik thats what i got but but not squared its 20.8
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
8.5
thats what I got

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