\( \mathrm{ABC} \) is a triangle having coordinates \( \mathrm{A}(\mathrm{c}, \mathrm{d}), \math...

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\( \mathrm{ABC} \) is a triangle having coordinates \( \mathrm{A}(\mathrm{c}, \mathrm{d}), \mathrm{B}(0,0) \) and \( \mathrm{C}(\mathrm{b}, 0) \) and \( \mathrm{O} \) is the point of intersection of the medians then \( \mathrm{AB}^{2}+\mathrm{BC}^{2}+\mathrm{CA}^{2} \) is equal to?
a. \( \left(\mathrm{OA}^{2}+\mathrm{OB}^{2}+\mathrm{OC}^{2}\right) \)
b. \( 3\left(\mathrm{OA}^{2}+\mathrm{OB}^{2}+\mathrm{OC}^{2}\right) \)
c. \( 5\left(\mathrm{OA}^{2}+\mathrm{OB}^{2}+\mathrm{OC}^{2}\right) \)
d. \( 7\left(\mathrm{OA}^{2}+\mathrm{OB}^{2}+\mathrm{OC}^{2}\right) \)
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