If ${p_1}, {p_2}, {p_3}$ are altitudes of a triangle $ABC$ from the vertices $A, B, C$ respectively and $\Delta$ is the area of the triangle,then ${p_1}^{-2} + {p_2}^{-2} + {p_3}^{-2}$ is equal to

  • A
    $\frac{a + b + c}{\Delta}$
  • B
    $\frac{a^2 + b^2 + c^2}{4\Delta^2}$
  • C
    $\frac{a^2 + b^2 + c^2}{\Delta^2}$
  • D
    None of these

Explore More

Similar Questions

If the angles of a triangle are in the ratio $1: 2: 3$,the corresponding sides are in the ratio

In any triangle $ABC$,$a \cdot \cos^2 \frac{A}{2} + b \cdot \cos^2 \frac{B}{2} + c \cdot \cos^2 \frac{C}{2} =$

In a $\triangle ABC$,it is known that $AB=AC$. Suppose $D$ is the mid-point of $AC$ and $BD=BC=2$. Then,the area of the $\triangle ABC$ is

With usual notation,in triangle $ABC$,$m \angle A = 30^{\circ}$. Then the value of $\left(1+\frac{a}{c}+\frac{b}{c}\right)\left(1+\frac{c}{b}-\frac{a}{b}\right)$ is equal to

In a triangle $ABC$,if $\frac{r}{r_1} = \frac{1}{2}$,then $4 \tan \frac{A}{2} \left( \tan \frac{B}{2} + \tan \frac{C}{2} \right) = $

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo