Embibe Experts Solutions for Exercise 15: EXERCISE 20.7

In a $∆ABC$, if $2 s=a+b+c$ and $\left(s-b\right)\left(s-c\right)=x{\sin }^2\frac{A}{2}$, then $x$ is equal to

If in $\Delta ABC, \sin \frac{A}{2}\sin \frac{C}{2}=\sin \frac{B}{2}$ and $2s$ is the perimeter of the triangle, then $s$ is

In any $∆ABC,\cot \frac{A}{2},\cot \frac{B}{2},\cot \frac{C}{2}$ are in $\mathrm{A}.\mathrm{P}.,$ then

$ABC$ is a right angled triangle with $\angle B=90°,a=6 \mathrm{cm}.$ If the radius of the circumcircle is $5\mathrm{cm},$ then the area of $\Delta ABC$ is

In an equilateral triangle of side $2\sqrt{3}\mathrm{cm},$ the circum-radius is

If $R$ is the radius of the circumcircle of the $\mathrm{\Delta }ABC$ and its area is $\mathrm{\Delta },$ then

In an equilateral triangle, the inradius and the circumradius are connected by

In $∆ABC,\angle A=\frac{\pi }{2},b=4,c=3$, then the value of $\frac{R}{r}$ is equal to