Let f, g, h be the lengths of the perpendicul | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $R$ be the circumradius of $\Delta ABC$. The perpendicular distance from the circumcentre to the side $a$ is $f = R \cos A$.Similarly,$g = R \

Vedclass · Accepted Answer

$1/4$

Vedclass · Answer

(A) Let $R$ be the circumradius of $\Delta ABC$. The perpendicular distance from the circumcentre to the side $a$ is $f = R \cos A$.Similarly,$g = R \cos B$ and $h = R \cos C$.We know that $a = 2R \sin A$,$b = 2R \sin B$,and $c = 2R \sin C$.Thus,$\frac{a}{f} = \frac{2R \sin A}{R \cos A} = 2 	an A$.Similarly,$\frac{b}{g} = 2 	an B$ and $\frac{c}{h} = 2 	an C$.Substituting these into the given equation: $2 	an A + 2 	an B + 2 	an C = \lambda \frac{(2R \sin A)(2R \sin B)(2R \sin C)}{(R \cos A)(R \cos B)(R \cos C)}$.$2(	an A + 	an B + 	an C) = \lambda \cdot 8 	an A 	an B 	an C$.In any triangle,$	an A + 	an B + 	an C = 	an A 	an B 	an C$.Therefore,$2(	an A 	an B 	an C) = 8 \lambda (	an A 	an B 	an C)$.$2 = 8 \lambda \Rightarrow \lambda = 1/4$.

Let $f, g, h$ be the lengths of the perpendiculars from the circumcentre of the $\Delta ABC$ on the sides $a, b$ and $c$ respectively. If $\frac{a}{f} + \frac{b}{g} + \frac{c}{h} = \lambda \frac{abc}{fgh}$,then the value of $\lambda$ is:

Similar Questions

With usual notation,in a triangle $ABC$,if $\frac{b+c}{11} = \frac{c+a}{12} = \frac{a+b}{13}$,then the value of $\cos B$ is equal to

In $\triangle ABC$,if $\frac{1}{b+c} + \frac{1}{c+a} = \frac{3}{a+b+c}$,then $\angle C$ is equal to: (in $^{\circ}$)

The perimeter of a $\triangle ABC$ is $6$ times the arithmetic mean of the values of the sine of its angles. If its side $BC$ is of unit length,then $\angle A=$

If $\tan \frac{B - C}{2} = x \cot \frac{A}{2},$ then $x = $

In triangle $ABC$,if $a, b, c$ are in $A.P.$,then the value of $\frac{\sin \frac{A}{2} \sin \frac{C}{2}}{\sin \frac{B}{2}} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module