In a $\Delta ABC$,a semicircle is inscribed,whose diameter lies on the side $c$. Then the radius of the semicircle is
Where $\Delta$ is the area of the triangle $ABC$.

In $\triangle ABC$,if $a=1, b=2, \angle C=60^{\circ}$,then find the value of $4 \Delta^2+c^2$.

Consider the following statements.
$I$. In $\triangle ABC$,if $c=6$ and $\cos C=-\frac{11}{25}$,then $R=\frac{25}{2\sqrt{14}}$.
$II$. In $\triangle ABC$,if $a=3, b=4, c=6$,then $\triangle ABC$ is an acute-angled triangle.
Which of the above statements is/are true?

Which of the following is true?

The angle bisectors $BD$ and $CE$ of a $\triangle ABC$ are divided by the incentre $I$ in the ratios $3:2$ and $2:1$ respectively. Then,the ratio in which $I$ divides the angle bisector through $A$ is

In a triangle $ABC$,if $\cos A \cos B + \sin A \sin B \sin C = 1$,then $a : b : c =$