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?

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) (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

But that distance is

So

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