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Question Number 75849 by behi83417@gmail.com last updated on 18/Dec/19

$$\mathbf{In}\mathbf{a}\mathbf{A}\stackrel{△}{\mathbf{B}\mathit{C}}:$$$$\{\begin{array}{l}\mathbf{a}+\mathbf{b}+\mathbf{c}=2({\mathbf{h}}_{\mathbf{a}}+{\mathbf{h}}_{\mathbf{b}}+{\mathbf{h}}_{\mathbf{c}})\\ {\mathbf{a}}^2+{\mathbf{b}}^2+{\mathbf{c}}^2=6\mathbf{abc}\\ {\mathbf{h}}_{\mathbf{a}}^2+{\mathbf{h}}_{\mathbf{b}}^2+{\mathbf{h}}_{\mathbf{c}}^2=6{\mathbf{h}}_{\mathbf{a}}.{\mathbf{h}}_{\mathbf{b}}.{\mathbf{h}}_{\mathbf{c}}\end{array}$$$$\mathbf{find}:\measuredangle \mathbf{A}$$

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