SOLUTION: Each of two congruent circles drawn in the interior of a square is tangent to two adjacent sides of the square and to the other circle, as shown in the diagram. If the Measure of a

Algebra ->  Circles -> SOLUTION: Each of two congruent circles drawn in the interior of a square is tangent to two adjacent sides of the square and to the other circle, as shown in the diagram. If the Measure of a      Log On


   

Question 363031: Each of two congruent circles drawn in the interior of a square is tangent to two adjacent sides of the square and to the other circle, as shown in the diagram. If the Measure of a side of the square is 16, find the radius of each circle.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

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From the diagram,
X%2BR=8
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X%5E2%2BX%5E2=R%5E2
2X%5E2=R%5E2
X=R%2Fsqrt%282%29
X=%28sqrt%282%29%2F2%29R
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%28sqrt%282%29%2F2%29R%2BR=8
R=8%2F%281%2Bsqrt%282%29%2F2%29
R=16%2F%282%2Bsqrt%282%29%29
highlight%28R=8%282-sqrt%282%29%29%29 or approximately,
R=4.69