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Rational Ratios and Concurrent Cevians

Antonio M. Oller-Marcén
Mathematics Magazine
Vol. 86, No. 4 (October 2013), pp. 265-269
DOI: 10.4169/math.mag.86.4.265
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Page Count: 5
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Rational Ratios and Concurrent Cevians
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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.

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