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More variations on Nagel and Gergonne analogues of the Steiner-Lehmus theorem
Published online by Cambridge University Press: 23 August 2024
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The celebrated Steiner-Lehmus theorem states that if the internal bisectors of two angles of a triangle are equal then the corresponding sides have equal lengths. That is to say if P is the incentre of ΔABC and if BP and CP meet the sides AC and AB at B′ and C′, respectively, then
An elegant proof of this theorem appeared in [1] and is reproduced in [2].
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- © The Authors, 2024 Published by Cambridge University Press on behalf of The Mathematical Association
References
Gilbert, G. and MacDonnel, D., The Steiner-Lehmus theorem, Amer. Math. Monthly 70 (October 1963) pp. 79–80.CrossRefGoogle Scholar
Abu-Saymeh, S., Hajja, M., More variations on the Steiner-Lehmus theme, Math. Gaz. 103 (March 2019) pp. 1–11.CrossRefGoogle Scholar
Sastry, K. R. S., A Gergonne analogue of the Steiner-Lehmus theorem, Forum Geom. 5 (2005) pp. 191–195.Google Scholar
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