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Tomahawk Trisection of an Angle

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Let . Let be a semicircle with diameter .

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Given any angle where is tangent to at , the straight lines and trisect .

In other words, the triangles , and are congruent.

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Contributed by: Izidor Hafner (September 2017)
Open content licensed under CC BY-NC-SA

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This Demonstration is based on [1]. The construction violates the Euclidean constraints on the use of only a straight edge and compass; specifically, by drawing the tangent . The result is true nonetheless since the semicircle radius and . Then .

Reference

[1] G. E. Martin, Geometric Constructions, New York: Springer, 1998 pp. 20–21.

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