Solution of Triangles

The circumradius of a triangle whose sides are 10 units, 8 units and 6 units is

In $\triangle A B C$, with usual notations, if the sides $a_{,} b$ and $c$ are in the ratio $18: 17: 7$, then $\cot \dfrac{A}{2}: \cot \dfrac{B}{2}: \cot \dfrac{C}{2}=$

In a triangle ABC with usual notations if, $\tan \left(\dfrac{B-C}{2}\right)=x \cot \dfrac{A}{2}$, then $x=$

In a triangle $A B C$, with usual notations, if $a=5, b=7 \sin A=\dfrac{3}{4}$, then total number of triangles possible are

In $\triangle A B C$, with usual notations, if $\cos A=\dfrac{1}{2}, a=3, \angle B=\dfrac{\pi^{c}}{6}$, then the values of $b$ and $c$ are.....

In a right-angled $\triangle A B C$, the measures of the angles are in an Arithmetic Progression (A.P.) If its smallest side is 4 units, then the area of $\triangle A B C$ is.....

In a triangle ABC with usual notations if $b \sin C(b \cos C+c \cos B)=42$, then area of triangle $\mathrm{ABC}=$

The angles of a triangle are in the ratio $5: 1: 6$, then ratio of the smallest side to the greatest side is

In $\triangle A B C$, with the usual notations, $\angle C=90^{\circ}$, then $\sin (A-B)$ is equal to....

In $\triangle A B C$, with usual notation, if $\cot A, \cot B, \cot C$ are in arithmetic progression, then

In triangle ABC , with usual notations, if $(a+b+c)(a+b-c)=a b$, then the measure of angle C is...

With the usual notations, if the lengths of the sides of the triangle are 3 units, 5 units and 7 units, then the largest angle of the triangle is

In a triangle ABC with usual notations, if $3 a=b+c$, then $\cot \dfrac{B}{2} \cdot \cot \dfrac{C}{2}=$

In a triangle ABC with usual notations, $\cot \dfrac{A}{2}+\cot \dfrac{B}{2}+\cot \dfrac{C}{2}=$

With usual notations in $\triangle \mathrm{ABC}$, if $\angle B=\dfrac{\pi}{2}$, and $\tan \dfrac{A}{2}, \tan \dfrac{C}{2}$ are roots of equation $\mathrm{p} x^{2}+\mathrm{qx}+\mathrm{r}=0, \mathrm{p} \neq 0$, then