Let $m_1, m_2, m_3$ be the slopes of the cartesian equations of the sides of a triangle of which no side is parallel to y-axis, and let $s_1,s_2,s_3$ be the slopes of the cartesian equations of the internal angle bisectors of the same triangle. The axes are orthogonal. Then we may say:
If $s_1,s_2,s_3$ are rational numbers, then $m_1, m_2, m_3$ are also rational numbers.
Any hints? This theorem seems a bit counterintuitive, because we cannot state the reverse or reciprocal of it.