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Constructing the Harmonic Mean 2

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This Demonstration shows a second construction of the harmonic mean .

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Draw perpendicular line segments and . Let the point be the intersection of the segment with the bisector of the angle . Let be the orthogonal projection of of the segment , and let be symmetric to with respect to . Then . Define . From the similarity of triangles and and the angle bisector property, we have , .

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Contributed by: Marko Razpet and Izidor Hafner (October 2018)
Open content licensed under CC BY-NC-SA

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