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If the lengths of the perpendiculars from the vertices of a triangle ABC on the opposite sides are `p_(1), p_(2), p_(3)` then prove that `(1)/(p_(1)) + (1)/(p_(2)) + (1)/(p_(3)) = (1)/(r) = (1)/(r_(1)) + (1)/(r_(2)) + (1)/(r_(3))`.

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