In a $\triangle ABC$,the expression $\frac{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}{4b^2c^2}$ equals:

In $\Delta ABC$,if $\cos \frac{A}{2} = \sqrt{\frac{b + c}{2c}}$,then:

In $\triangle ABC$,with usual notations,$\frac{b \sin B - c \sin C}{\sin (B - C)} = $

Let $a, b$ and $c$ be the lengths of the sides of a triangle $ABC$ such that $\frac{a+b}{7} = \frac{b+c}{8} = \frac{c+a}{9}$. If $r$ and $R$ are the inradius and circumradius of the triangle $ABC$,respectively,then the value of $\frac{R}{r}$ is equal to

With usual notations, in $\triangle ABC$, if $\cos C = \frac{\sin A}{2 \sin B}$, then which of the following is true?

The angles of a triangle are in the ratio $3: 5: 10$. Then the ratio of the smallest side to the greatest side is: