If {p_1}, {p_2}, {p_3} are altitudes of a tri | vedclass

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(B) The area of triangle $ABC$ is given by $\Delta = \frac{1}{2} a p_1 = \frac{1}{2} b p_2 = \frac{1}{2} c p_3$.From this,we get $p_1 = \frac{2\Delta}

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$\frac{a^2 + b^2 + c^2}{4\Delta^2}$

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(B) The area of triangle $ABC$ is given by $\Delta = \frac{1}{2} a p_1 = \frac{1}{2} b p_2 = \frac{1}{2} c p_3$.From this,we get $p_1 = \frac{2\Delta}{a}$,$p_2 = \frac{2\Delta}{b}$,and $p_3 = \frac{2\Delta}{c}$.Therefore,${p_1}^{-2} + {p_2}^{-2} + {p_3}^{-2} = \frac{1}{p_1^2} + \frac{1}{p_2^2} + \frac{1}{p_3^2}$.Substituting the values,we get $\frac{a^2}{4\Delta^2} + \frac{b^2}{4\Delta^2} + \frac{c^2}{4\Delta^2} = \frac{a^2 + b^2 + c^2}{4\Delta^2}$.

If ${p_1}, {p_2}, {p_3}$ are altitudes of a triangle $ABC$ from the vertices $A, B, C$ respectively and $\Delta$ is the area of the triangle,then ${p_1}^{-2} + {p_2}^{-2} + {p_3}^{-2}$ is equal to

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