28 – semicircles problem and block game

At least once a week, I have my students work on a group PS. Today my geometry class started on this problem (can’t remember where I got it):

In the figure below, ABCD is a square. The four semicircles are congruent and each is tangent to two of its neighbors. Each side of the square contains the diameter of one of the semicircles and is tangent to another.


Assume the radius of each semicircle to be 1. What is the ratio of the diameter one of the semicircles to the side-length of the square?

We didn’t get too far in this problem. More next time.

My 6th graders worked on adding and subtracting integers via Block Game.


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