• # question_answer If $\alpha ,\,\,\beta$ and $\gamma$ are the altitudes of the $\Delta ABC$ from the vertices A, B and C respectively, then value of $4{{\Delta }^{2}}\,\left( \frac{1}{{{\alpha }^{2}}}+\frac{1}{{{\beta }^{2}}}+\frac{1}{{{\gamma }^{2}}} \right)$ is A)  ${{a}^{2}}+{{b}^{2}}+{{c}^{2}}$             B)  $\frac{1}{2}\,({{a}^{2}}+{{b}^{2}}+{{c}^{2}})$ C)  ${{a}^{2}}-{{b}^{2}}+{{c}^{2}}$               D)  $\frac{3}{\Delta }$

Clearly, ${{X}_{CM}}$ ${{m}_{2}}{{x}_{2}}=-{{m}_{1}}{{x}_{1}}$ $\therefore$ ${{x}_{2}}=\frac{{{m}_{1}}}{{{m}_{2}}}{{x}_{1}}$