Geometry Problem 295

Archimedean Twin Circles, Arbelos, Semicircles, Harmonic Mean, Radii, Perpendicular

Poster of Geometry Problem 295: Archimedes Twin Circles, Archimedean, Semicircles, Diameters, Harmonic Mean, iPad Apps, Typography. Math Infographic, Tutor


The figure shows the semicircles of diameters AB (center O), AC (center D, radius a), and BC (center E, radius b). Prove that radii of circles G (radius x) and H (radius y) inscribed in ACF and CBF, respectively, are equal to one-half the harmonic mean of a and b, that is: \(x=y = \dfrac{a \cdot b}{(a+b)}=\dfrac{1}{2} \cdot H(a,b)\).

The figure included between the circumferences of the three semicircles is "what Archimedes called arbelos."

Geometry Problem 295: Archimedes Twin Circles, Arbelos, Harmonic Mean, Math Infographic, Tutor

Geometric Art using iPad or Mobile Apps

Geometric art is a form of art based on the use and application of geometric figures. A geometric figure is any set or combination of points, lines, surfaces and solids.

A mobile app or mobile application software is a computer program designed to run on smartphones and tablet computers.