$$ \text { In } \triangle A B C, \frac{r_2\left(r_1+r_3\right)}{\sqrt{r_1 r_2+r_2 r_3+r_3 r_1}} \text { is equal to } $$

In $a \triangle A B C$ if $r: R: r_2=1: 3: 7$, then $\sin (A+C)+\sin B$ is equal to

In $\triangle A B C,\left(r_1+r_2\right) \operatorname{cosec}^2 \frac{C}{2}$ is equal to

In a $\triangle A B C$, if $A, B$ and $C$ are in arithmetic progression and $\cos A+\cos B+\cos C=\frac{1+\sqrt{2}+\sqrt{3}}{2 \sqrt{2}}$, then $\tan A$ :

In $\triangle A B C$, if $b+c: c+a: a+b=7: 8: 9$, then the smaller angle (in radians) of that triangle is

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

In a $$\triangle A B C$$, if $$r_1=36, r_2=18$$ and $$r_3=12$$, then $$s=$$

In a $$\triangle A B C, a=6, b=5$$ and $$c=4$$, then $$\cos 2 A=$$

In a $$\triangle A B C,\left(\tan \frac{A}{2} \tan \frac{B}{2} \tan \frac{C}{2}\right)^2 \leq$$

In a $$\triangle A B C, 2(b c \cos A+a c \cos B+a b \cos C)=$$

In a $$\triangle A B C, \frac{a}{b}=2+\sqrt{3}$$ and $$\angle C=60^{\circ}$$. Then, the measure of $$\angle A$$ is

If $$a=2, b=3, c=4$$ in a $$\triangle A B C$$, then $$\cos C=$$

In a $$\triangle A B C$$ $$(b+c) \cos A+(c+a) \cos B+(a+b) \cos C=$$

Suppose $$\triangle A B C$$ is an isosceles triangle with $$\angle C=90^{\circ}, A=(2,3)$$ and $$B=(4,5)$$. Then, the centroid of the triangle is

In a $$\triangle A B C$$, if $$a \neq b, \frac{a \cos A-b \cos B}{a \cos B-b \cos A}+\cos C=$$

If in a $$\triangle A B C, a=2, b=3$$ and $$c=4$$, then $$\tan (A / 2)=$$

If the angles of a $$\triangle A B C$$ are in the ratio $$1: 2: 3$$, then the corresponding sides are in the ratio

In a $$\triangle A B C, r_1 \cot \frac{A}{2}+r_2 \cot \frac{B}{2}+r_3 \cot \frac{C}{2}=$$

In $$\triangle A B C$$, medians $$A D$$ and $$B E$$ are drawn. If $$A D=4, \angle D A B=\frac{\pi}{6}$$ and $$\angle A B E=\frac{\pi}{3}$$, then the area of $$\triangle A B C$$ is

In a $$\triangle A B C, 2 \Delta^2=\frac{a^2 b^2 c^2}{a^2+b^2+c^2}$$, then the triangle is

In $$\triangle A B C$$, suppose the radius of the circle opposite to an angle $$A$$ is denoted by $$r_1$$, similarly $$r_2 \leftrightarrow$$ angle $$B, r_3 \leftrightarrow$$ angle $$C$$. If $$r_1=2, r_2=3, r_3=6$$, what is the value of $$r_1+r_2+r_3-r=$$ (R - radius of the circum circle).

In a $$\Delta ABC$$, if a = 3, b = 4 and $$\sin A=\frac{3}{4}$$, then $$\angle CBA$$ is equal to

In $$\Delta ABC,A=75\Upsilon$$ and $$B=45\Upsilon$$, then the value of $$b+c\sqrt2$$ is equal to

In $$\triangle A B C$$, suppose the radius of the circle opposite to an $$\angle A$$ is denoted by $$r_1$$, similarly $$r_2 \leftrightarrow \angle B$$ and $$r_3 \leftrightarrow \angle C$$. If $$r$$ is the radius of inscribed circle, then, what is the value of $$\frac{a b-r_1 r_2}{r_3}$$ is equal to

If D, E and F are respectively mid-points of AB, AC and BC in $$\Delta ABC$$, then BE + AF is equal to