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If p(1),p(2),p(3) are the altitues of a ...

If `p_(1),p_(2),p_(3)` are the altitues of a triangle from the vertieces A,B,C and `Delta` is the area of the triangle then prove that
`(1)/(p_(1))+(1)/(p_(2))+(1)/(p_(3))=(2ab)/((a+b+c+)Delta)"cos"^(2)(C)/(2)`

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