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Geometry Problem 20 with Solution: Right triangle, Altitude, Perpendiculars, Inradii, Similarity,
Geometric Mean.
Sketch, Software.
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In triangle ABC, angle B is a right angle. BD is the altitude,
DE is perpendicular to AB and DF is perpendicular to BC.
a, b, and x are the
inradii of the triangles AED, DFC and EDF respectively. Prove that x is the geometric mean of
a and b that is: \(x = \sqrt{a \cdot b}\).
See solution below
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Sketch of problem 20 using iPad Apps.
Art of Geometry Problem 20 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
the
kaleidoscope of problem
20.
See
also:
Problem art
20
Sketch problem
20 art 1
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