Consider a plane passing through three points \( \mathrm{A}(\mathrm...

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Consider a plane passing through three points \( \mathrm{A}(\mathrm{a}, 0,0), \mathrm{B}(0, \mathrm{~b}, 0), \mathrm{C}(0,0, \mathrm{c}) \) with \( \mathrm{a}0, \mathrm{~b}0 \), \( \mathrm{c}0 \). Let \( \mathrm{d} \) be the distance between the origin \( \mathrm{O} \) and the plane and \( \mathrm{m} \) be the distance
\( \mathrm{P} \) between the origin \( \mathrm{O} \) and the point \( \mathrm{M}(\mathrm{a}, \mathrm{b}, \mathrm{c}) \). If \( \mathrm{a}, \mathrm{b}, \mathrm{c} \) vary in the range of any positive

W numbers, then find the minimum value of \( \left(\frac{\mathrm{m}}{\mathrm{d}}\right)^{2} \).
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