Question

If $P_1,P_2$ and $P_3$ are the altitudes of a triangle from vertices $A,B$ and $C$ respectively and $\Delta$ is the area of the triangle, then the value of $\frac{1}{P_1}+\frac{1}{P_2}-\frac{1}{P_3}=$

• A. $\frac{2(S-C)}{\Delta }$
• B. $\frac{S-C}{2\Delta }$
• C. $\frac{S-C}{\Delta }$
• D. $noneofthese$

Answer 1

Answer: (D)

$noneofthese$

$P_1=\frac{2△}{a};P_2=\frac{2△}{b};P_3=\frac{2△}{c}$

$\therefore \frac{1}{P_1}+\frac{1}{P_2}-\frac{1}{P_3}=\frac{a+b-c}{2△}$

$=\frac{s-2c}{△}$ -Option D