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Question Number 173426 by Shrinava last updated on 11/Jul/22

$$\mathrm{In}△\mathrm{ABC}\mathrm{the}\mathrm{following}\mathrm{relationship}$$$$\mathrm{holds}:$$$$({\mathrm{a}}^3+{\mathrm{b}}^3+{\mathrm{c}}^3)({\mathrm{h}}_{\mathbf{a}}^3+{\mathrm{h}}_{\mathbf{b}}^3+{\mathrm{h}}_{\mathbf{c}}^3)⩾5832\sqrt{3}{\mathrm{r}}^6$$

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