SOLUTION: ABCD is a square. Four congruent semicircles all have radii 1 and have centers at midpoints on the sides of the square. Semicircles are tangent pairwise and small circle is tangent

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Question 1101137: ABCD is a square. Four congruent semicircles all have radii 1 and have centers at midpoints on the sides of the square. Semicircles are tangent pairwise and small circle is tangent to all of them. What is the radius of the small circle?
Found 2 solutions by Edwin McCravy, AnlytcPhil:
Answer by Edwin McCravy(20059)   (Show Source): You can put this solution on YOUR website!



Draw in the red line and the two green lines:



The red line is composed of two radii of length 1 each.
Therefore the red line has length 2.

The green lines are the equal length legs of an isosceles right triangle 
with red hypotenuse of length 2.

Therefore the green lines each have length 

Each green line is made up of a radii of length 1, plus the
radius of the small circle.

Therefore the radius of the small circle is .

Edwin
Answer by AnlytcPhil(1806)   (Show Source): You can put this solution on YOUR website!

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