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If \( p_{1}, p_{2}, p_{3} \) are altitudes of a triangle \( A B C \) from the vertices \( A, B, C \) and \( \Delta \), the area of the triangle, then \( p_{1}^{2}+p_{2}{ }^{-2}+p_{3}{ }^{-2} \) is equal to
(A) \( \frac{a+b+c}{\Delta} \)
(B) \( \frac{a^{2}+b^{2}+c^{2}}{\Delta^{2}} \)
(C) \( \frac{a^{2}+b^{2}+c^{2}}{4 \Delta^{2}} \)
(D) none of these
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