K-Lemoine-s-I-incenter-in-ABC-Prove-that-KA-4-KB-4-KC-4-IA-4-IB-4-IC-4-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 181625 by Shrinava last updated on 27/Nov/22

K-Lemoine′s , I-incenter in △ABC. Prove that: KA^4 +KB^4 +KC^4 ≥ IA^4 +IB^4 +IC^4

$$\mathrm{K}-\mathrm{Lemoine}'\mathrm{s}\:,\:\mathrm{I}-\mathrm{incenter}\:\mathrm{in}\:\bigtriangleup\mathrm{ABC}. \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{KA}^{\mathrm{4}} +\mathrm{KB}^{\mathrm{4}} +\mathrm{KC}^{\mathrm{4}} \:\geqslant\:\mathrm{IA}^{\mathrm{4}} +\mathrm{IB}^{\mathrm{4}} +\mathrm{IC}^{\mathrm{4}} \\ $$

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K-Lemoine-s-I-incenter-in-ABC-Prove-that-KA-4-KB-4-KC-4-IA-4-IB-4-IC-4-

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