SOLUTION: A circle of radius 6 cm is inscribed in a square. A smaller circle is drawn tangent to the two sides of the square and the bigger circle. What is the radius of the smaller circle?

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Question 1146415: A circle of radius 6 cm is inscribed in a square. A smaller circle is drawn tangent to the two sides of the square and the bigger circle. What is the radius of the smaller circle?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Draw the figure as described.

Draw 3 radii of the smaller circle -- perpendicular to the two sides of the square, and to the point of tangency of the two circles.

Calling r the radius of the small circle, the distance from the center of the large circle to the corner of the square is

6%2Br%2Br%2Asqrt%282%29

But that distance is 6%2Asqrt%282%29

So

6%2Br%2Br%2Asqrt%282%29+=+6%2Asqrt%282%29
6%2Br%281%2Bsqrt%282%29%29+=+6%2Asqrt%282%29
r%281%2Bsqrt%282%29%29+=+6%2Asqrt%282%29-6+=+6%28sqrt%282%29-1%29
r+=+%286%28sqrt%282%29-1%29%29%2F%28sqrt%282%29%2B1%29

r+=+6%283-2%2Asqrt%282%29%29%2F%282-1%29
r+=+6%283-2%2Asqrt%282%29%29