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Prove this geometric inequality for external and internal bisector

Source: 2019 Jozsef Wildt International Math Competition

May 20, 2020
geometryTriangleangle bisectorgeometric inequalityinequalitiescircumradiusinradius

Problem Statement

Denote wa‾,wb‾,wc‾\overline{w_a}, \overline{w_b}, \overline{w_c} the external angle-bisectors in triangle ABCABC, prove that ∑cyc1wa≤(s2−r2−4Rr)(8R2−s2−r2−2Rr)8s2R2r\sum \limits_{cyc} \frac{1}{w_a}\leq \sqrt{\frac{(s^2 - r^2 - 4Rr)(8R^2 - s^2 - r^2 - 2Rr)}{8s^2R^2r}}
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