If r is the inradius,Delta is the area of tri | vedclass

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

Question

(D) Let the lengths of the sides of $	riangle ABC$ be $a, b,$ and $c$. The semi-perimeter $s$ is given by $s = \frac{a+b+c}{2}$.From the diagram,the

Vedclass · Accepted Answer

$\Delta = rs$

Vedclass · Answer

(D) Let the lengths of the sides of $	riangle ABC$ be $a, b,$ and $c$. The semi-perimeter $s$ is given by $s = \frac{a+b+c}{2}$.From the diagram,the area of $	riangle ABC$ can be expressed as the sum of the areas of $	riangle IBC, 	riangle ICA,$ and $	riangle IAB$,where $I$ is the incenter:$\Delta = 	ext{Area}(	riangle IBC) + 	ext{Area}(	riangle ICA) + 	ext{Area}(	riangle IAB)$$\Delta = \frac{1}{2}ar + \frac{1}{2}br + \frac{1}{2}cr$$\Delta = r \left( \frac{a+b+c}{2} ight)$Since $s = \frac{a+b+c}{2}$,we have $\Delta = rs$.Thus,option $(d)$ is correct.

If $r$ is the inradius,$\Delta$ is the area of $\triangle ABC$,and $s$ is the semi-perimeter,then which of the following is true?

Similar Questions

In a $\triangle ABC$,let $\angle C = \frac{\pi}{2}$. If $r$ and $R$ are the inradius and circumradius of $\triangle ABC$ respectively,then $R+r=$

In $\triangle ABC$,if $a=13 \text{ cm}, b=14 \text{ cm}$ and $c=15 \text{ cm}$,then its circumradius $R$ is:

The circumradius of triangle $PRS$ is . . . . .

In a triangle $ABC$,if $b = 2$ and $B = 30^\circ$,then the area of the circumcircle of triangle $ABC$ in square units is:

If the roots of the equation $x^3-11x^2+36x-36=0$ are the ex-radii of a triangle $ABC$,then the perimeter of the triangle $ABC$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module