In the diagram below, given a
semicircle of diameter AB, CD is a perpendicular to AB, circle
of diameter CD and semicircles of diameter AC and CB
respectively. If S1, S2, S3 , S4,
and S5 are the shaded areas, prove that: S1
+ S2 + S3 = S4 + S5.
Archimedes' Book of Lemmas:
Proposition 4 Arbelos.
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Artist's impression of Oumuamua, the first known interstellar object to pass through the Solar System. Photograph: ESO/M. Kornmesser/PA.