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| | Math Forum - Ask Dr. Math |
 | | We will use the Law of Sines, which states that a b c ----- = ----- = ----- = 2R sin(A) sin(B) sin(C) and thus, for instance, also a = 2R sin(A) where a = BC, b = AC, c = AB, and R is the radius of the circumcircle of triangle ABC. |
 | | Well, if we let a', b', c' be given so that a' + b' + c' = 60 deg, so that a', b', and c' are the trisected angles of a given triangle. |
 | | And we conclude that ABC is a triangle with the same angles as the given triangle, and that the angle trisectors intercept an equilateral triangle. |
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