Typography of Geometry Problem 1103: Right Triangle, Incircle, Inscribed Circle, Radius, Geometric Mean, iPad Apps

Proposition

In a right triangle ABC (see the figure below) incircle O (radius r) is tangent to BC, AC, and AB at D, E, and F, respectively. Circle O₁ (radius r₁) is inscribed in quadrilateral AFOE and circle O₂ (radius r₂) is inscribed in quadrilateral CDOE. Prove that r² = 2r₁.r₂.

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Geometric Art using 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.

See also:
Original problem 1103.