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The circle can be cut into just four pieces:
Let the center of the circle be O. Draw any diameter with endpoints P and Q. Choose point A on OP and choose point B on OQ.
Construct a rectangle using AB as a base and with a height small enough so that the rectangle is entirely inside the circle. Label the other two points on the rectangle C and D so that AC and BD are perpendictular to AB.
On the other side of the diameter construct rectangle ABEF with AE and BF perpendictular to AB and also having a shorter length than AC (and BD).
A, C and E are colinear with AC>AE; B, D and F are colinear with BD>BF. Choose point G on AC so that CG = AE and choose point H on BD so that DH = BF. Rectangle CDGH is congruent to ABEF.
The circle can be cut along lines PA, QB, CE, DF, CD, DF, GH, none of which contain O. The piece defined by cuts along PACDBQ plus rectangle piece EFGH form one semicircle and the piece defined by cuts along PAEFBQ plus rectangle CDGH form the second semicircle. |
