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REFERENCES
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Mohammad K. Azarian, A Trigonometric Characterization of Equilateral Triangle, Problem 336, Mathematics and Computer Education, Vol. 31, No. 1, Winter 1997, p. 96. Solution published in Vol. 32, No. 1, Winter 1998, pp. 84-85.
Mohammad K. Azarian, Equating Distances and Altitude in an Equilateral Triangle, Problem 316, Mathematics and Computer Education, Vol. 28, No. 3, Fall 1994, p. 337. Solution published in Vol. 29, No. 3, Fall 1995, pp. 324-325.
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EXAMPLE
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a(2)=1: The 3 line segments intersect each other at the triangle center (r=0).
a(3)=3: There are 3 intersection points at r=0.2, 3 at r=0.25 and 6 at r=0.3779645, i.e. 3 different radii. See pictures given at link.
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