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Geometry Problem 100. Circle Area, Archimedes' Book of Lemmas, Arbelos, Areas. Level: School, College, Mathematics Education


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.

Circle Area, Archimedes Book of Lemmas, Arbelos, Areas

See also:
Archimedes' Book of Lemmas: Proposition 4 Arbelos

Typography Art of Problem 100 using Mobile Apps, iPad Software

Typography of Geometry Problem 100, Circle Area, Archimedes Book of Lemmas, Arbelos, Areas using Mobile Apps, iPad

Background: Artist's impression of Oumuamua, the first known interstellar object to pass through the Solar System. Photograph: ESO/M. Kornmesser/PA.

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