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

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

Answer by jim_thompson5910(35256) (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 units. So that means

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 )

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

Now plug in (we solved for this earlier)

Foil

Evaluate to get 225

Subtract from both sides

Subtract 81 from both sides

Combine like terms

Divide both sides by 18

Now plug back into

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