SOLUTION: Find x and y http://i112.photobucket.com/albums/n168/daddygirl411/mathcircle2.jpg

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Question 92723: Find x and y
http://i112.photobucket.com/albums/n168/daddygirl411/mathcircle2.jpg

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
Since the segment labeled "y" makes up the radius, this means the radius is y units. Also the segments labeled "9" and "x" make up the radius, this means the the radius is x%2B9 units. So that means y=x%2B9




Now lets look at the upper triangle
The vertical leg is equal to half of the chord length. So the vertical leg is 15 units (since the chord is bisected, ie 30%2F2=15)

drawing%28500%2C500%2C-3%2C3%2C-2%2C3%2C%0D%0A%0D%0Aline%280%2C3%2C-2%2C0%29%2C%0D%0Aline%28-2%2C0%2C0%2C0%29%2C%0D%0Aline%280%2C0%2C0%2C3%29%2C%0D%0Alocate%280.2%2C1.5%2C15%29%2C%0D%0Alocate%28-1%2C-0.05%2Cx%29%2C%0D%0Alocate%28-1%2C2%2Cy%29%0D%0A%29

So by looking at the triangle, we can use Pythagoreans Theorem to express y in terms of x like this:

y%5E2=x%5E2%2B15%5E2

Now plug in y=x%2B9 (we solved for this earlier)

%28x%2B9%29%5E2=x%5E2%2B15%5E2


x%5E2%2B18x%2B81=x%5E2%2B15%5E2 Foil

x%5E2%2B18x%2B81=x%5E2%2B225Evaluate 15%5E2 to get 225

x%5E2%2B18x%2B81-x%5E2=225 Subtract x%5E2 from both sides


x%5E2%2B18x-x%5E2=225-81 Subtract 81 from both sides

18x=144 Combine like terms


x=8 Divide both sides by 18


Now plug x=8 back into y=x%2B9

y=8%2B9=17

So the radius is 17 units where x=8 and y=17