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Rational Ratios and Concurrent Cevians
Antonio M. Oller-Marcén
Vol. 86, No. 4 (October 2013), pp. 265-269
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.86.4.265
Page Count: 5
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Summary Euler, in a paper published in 1812, studied in detail the situation when three cevians of a triangle were concurrent. In particular, he found a relation between the ratios in which the common point divided each of the cevians. This relation can be seen as an equation in three unknowns (the three ratios). In this paper we find the integer and rational solutions of this equation, providing explicit constructions and geometric interpretations in the positive cases.
Copyright the Mathematical Association of America 2013