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Proof 4.30

The Salinon (p. 98)
a. The diagram above is a Salinon as described in the text. b. The area of a circle can be determined by  where r is the radius of the circle. The Salinon is created by semicircles so the area of Salinon is  because  by construction.  c. The perpendicular bisector of  is constructed as described in the book which creates the circle MN. d. The area of MN is found using the same formula from above. The area of the circle MN is  because  is a line length and has no area by the definition of a line and by construction we know that the radii of the original circle all have equal length so we can write the value of  in terms of P,Q, R, and S. Also notice, . Therefore,