Bart De Bruyn, On a Problem Regarding the $n$-Sectors of a Triangle,
Forum Geometricorum, 5 (2005) 47--52.

Abstract: Let Delta be a triangle with vertices A, B, C and angles alpha, beta, gamma. The n-1 lines through A which, together with the lines AB and AC, divide the angle alpha in n >= 2 equal parts are called the n-sectors of  Delta. In this paper we determine all triangles with the property that all three edges and all 3(n-1)  n-sectors have rational lengths. We show that such triangles exist only if  n = 2, 3.

[ps file][pdf file]

Return to Forum Geometricorum, volume 5.