SOLUTION: A circle is inscribed in a right angle triangle. The circle touches the hypotenuse, dividing it in the ratio 3:2. find the radius of the circle?

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Question 902633: A circle is inscribed in a right angle triangle. The circle touches the
hypotenuse, dividing it in the ratio 3:2. find the radius of the circle?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
No dimensions are given, only the 3:2 ratio, so I can only 
assume that the hypotenuse is 5 units long and is divided 
into two parts, one which is 3 units long and the other 
2 units long, like this drawing. Let the radius be R units
long: 



So by the Pythagorean theorem:

%283%2BR%29%5E2%2B%28R%2B2%29%5E2+=+%283%2B2%29%5E2

9%2B6R%2BR%5E2%2BR%5E2%2B4R%2B4=5%5E2

2R%5E2%2B10R%2B13=25

2R%5E2%2B10R-12=0

Divide through by 2:

R%5E2%2B5R-6=0

%28R%2B6%29%28R-1%29=0

R%2B6=0, R-1=0
  R=-6,  R=1

We ignore the negative answer, and
the radius is R = 1 unit long.

Anything you don't understand you can ask 
me in the thank-you note below and I will 
get back to you.

Edwin