SOLUTION: Two circles touch externally with their radius being 25 and 9 cm. A common tangent is drawn.another circle touching both the circles and the tangent is drawn.what is the radius of

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Question 975649: Two circles touch externally with their radius being 25 and 9 cm. A common tangent is drawn.another circle touching both the circles and the tangent is drawn.what is the radius of that small circle
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for this problem is derived on this website:

analyzemath.com/Geometry/challenge/three_circles_problem.html

It is:

c%22%22=%22%22a%2Ab%2F%28sqrt+%28b%29%2B+sqrt%28a%29%29%5E2%29

where c = the small circle's radius, and a and b are the radii of the 
other two circles, in this case 25 and 9.

c%22%22=%22%2225%2A9%2F%28sqrt+%2825%29%2B+sqrt%289%29%29%5E2%29%22%22=%22%22225%2F%285%2B3%29%5E2%22%22=%22%22225%2F8%5E2%22%22=%22%22225%2F64

Edwin