The angles of a triangle are in the ratio $2:3:7$ and the radius of the circumscribed circle is $10 \text{ cm}$. The length of the smallest side is (in $\text{ cm}$)

Let $ABC$ be a triangle such that $AB = BC$. Let $F$ be the mid-point of $AB$ and $X$ be a point on $BC$ such that $FX$ is perpendicular to $AB$. If $BX = 3XC$,then the ratio $BC / AC$ equals

In a $\triangle ABC$,if $\tan(A/2)$,$\tan(B/2)$,and $\tan(C/2)$ are in Arithmetic Progression,then which of the following options is always correct?

In a triangle $ABC$ with usual notations,find the value of $\cot \frac{A}{2} + \cot \frac{B}{2} + \cot \frac{C}{2}$.

In a $\triangle ABC$,$\frac{2(r_1+r_3)}{ac(1+\cos B)} = $

In a $\Delta ABC$,if ${r_1} < {r_2} < {r_3}$,then: