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Question Number 187691 by normans last updated on 21/Feb/23

$$$$$$\mathit{M}\mathit{i}\mathit{s}\mathit{a}\mathit{l}\mathit{k}\mathit{a}\mathit{n}\mathit{P}\mathit{s}\mathit{e}\mathit{b}\mathit{a}\mathit{r}\mathit{a}\mathit{n}\mathit{g}\mathit{t}\mathit{i}\mathit{t}\mathit{i}\mathit{k}\mathit{d}\mathit{i}\mathit{d}\mathit{a}\mathit{l}\mathit{a}\mathit{m}\mathbf{\Delta }\mathit{A}\mathit{B}\mathit{C}\mathit{s}\mathit{e}\mathit{h}\mathit{i}\mathit{n}\mathit{g}\mathit{g}\mathit{a}\mathit{P}\mathit{D},\mathit{P}\mathit{E},\mathit{d}\mathit{a}\mathit{n}\mathit{P}\mathit{F}$$$$\mathit{m}\mathit{a}\mathit{s}\mathit{i}\mathit{n}\mathit{g}\mathit{m}\mathit{a}\mathit{s}\mathit{i}\mathit{n}\mathit{g}\mathit{t}\mathit{e}\mathit{g}\mathit{a}\mathit{k}\mathit{l}\mathit{u}\mathit{r}\mathit{u}\mathit{s}\mathit{d}\mathit{e}\mathit{n}\mathit{g}\mathit{a}\mathit{n}\mathit{s}\mathit{i}\mathit{s}\mathit{i}\mathit{B}\mathit{C},\mathit{C}\mathit{A}\mathit{d}\mathit{a}\mathit{n}\mathit{A}\mathit{B}$$$$\mathit{J}\mathit{i}\mathit{k}\mathit{a}\mathit{p}\mathit{a}\mathit{n}\mathit{j}\mathit{a}\mathit{n}\mathit{g}\mathit{s}\mathit{i}\mathit{s}\mathit{i}\mathit{B}\mathit{C},\mathit{C}\mathit{A}\mathit{d}\mathit{a}\mathit{n}\mathit{A}\mathit{B}$$$$\mathit{m}\mathit{a}\mathit{s}\mathit{i}\mathit{n}\mathit{g}\mathit{m}\mathit{a}\mathit{s}\mathit{i}\mathit{n}\mathit{g}\mathit{d}\mathit{i}\mathit{n}\mathit{o}\mathit{t}\mathit{a}\mathit{s}\mathit{i}\mathit{k}\mathit{a}\mathit{n}\mathit{d}\mathit{e}\mathit{n}\mathit{g}\mathit{a}\mathit{n}\mathit{a},\mathit{b}\mathit{d}\mathit{a}\mathit{n}\mathit{c}.$$$$\mathit{b}\mathit{i}\mathit{l}\mathit{a}\mathit{x},\mathit{y}\mathit{d}\mathit{a}\mathit{n}\mathit{z}\mathit{a}\mathit{d}\mathit{a}\mathit{l}\mathit{a}\mathit{h}\mathit{s}\mathit{e}\mathit{b}\mathit{a}\mathit{r}\mathit{a}\mathit{n}\mathit{g}\mathit{b}\mathit{i}\mathit{l}\mathit{a}\mathit{n}\mathit{g}\mathit{a}\mathit{n}\mathit{r}\mathit{e}\mathit{a}\mathit{l}\mathit{y}\mathit{a}\mathit{n}\mathit{g}\mathit{m}\mathit{e}\mathit{m}\mathit{e}\mathit{n}\mathit{u}\mathit{h}\mathit{i}\mathit{x}\mathit{y}+\mathit{y}\mathit{z}+\mathit{x}\mathit{z}⩾0$$$$\mathit{T}\mathit{u}\mathit{n}\mathit{j}\mathit{u}\mathit{k}\mathit{k}\mathit{a}\mathit{n}\mathit{b}\mathit{a}\mathit{h}\mathit{w}\mathit{a};$$$$(\mathit{y}+\mathit{z})\frac{\mathit{P}\mathit{A}}{\mathit{a}}+(\mathit{z}+\mathit{x})\frac{\mathit{P}\mathit{B}}{\mathit{b}}+(\mathit{x}+\mathit{y})\frac{\mathit{P}\mathit{C}}{\mathit{c}}⩾2\sqrt{\mathit{x}\mathit{y}+\mathit{y}\mathit{z}+\mathit{z}\mathit{x}}$$$$$$

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