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If $P_{1}, P_{2} and P_{3}$ are the lenths of th altitudes drawn from the vertices A,B and C of $∆ A B C$ respectively,then $\frac{\cos A}{P_{1}} + \frac{\cos B}{P_{2}} + \frac{\cos C}{P_{3}} =$

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$\frac{1}{R}$

$\frac{Δ}{R}$

$\frac{r}{R}$

answer is A.

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Detailed Solution

Area of triangle $Δ = \frac{1}{2} AP$

$\frac{1}{P_{1}} = \frac{a}{2 Δ}$

similarly

$\frac{1}{P_{2}} = \frac{b}{2 Δ} and \frac{1}{p_{3}} = \frac{c}{2 Δ}$

write the standard results will get

$\frac{\cos A}{P_{1}} + \frac{\cos B}{P_{2}} + \frac{\cos C}{P_{3}} = = \frac{1}{R}$

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