The figure below shows a square ABCD of
center O, side "a" and area "S". Circles of centers A (radius
AO) and C (radius CB) meet at E and E'. Circles of center B
(radius BO) and D (radius DA) meet at F and F'. S_{1} is the area
of triangle EOF. Prove that
(1)
;
(2) angle EOF = 90 degrees; (3)
.