Area of a triangle and angle bisectors

Published 27 May 2020 in math.GR | (2005.13431v1)

Abstract: Consider a triangle $ABC$ with given lengths $l_a,l_b,l_c$ of its internal angle bisectors. We prove that in general, it is impossible to construct a square of the same area as $ABC$ using a ruler and compass. Moreover, it is impossible to express the area of $ABC$ in radicals of $l_a,l_b,l_c$.

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