Question

If a,b,y are the altitudes of a $△ABC$ and 2s denotes its perimeter,
then $a^{-1}+B^{-1}+y^{-1}$ is equal to

• A.
• B.
• C.
• D. None of these

Answer 1

The correct option is B

$\frac{1}{2}.a.a=△$
$\therefore \frac{1}{a}=\frac{a}{2△}$
Similarly, $\frac{1}{B}=\frac{b}{2△},\frac{1}{2}=\frac{c}{2△}$
$\therefore a^{-1}+B^{-1}+y^{-1}=\frac{1}{2△}(a+b+c)=\frac{S}{△}$