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.

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