If two sides of a triangle are $\sqrt{3}-2$ and $\sqrt{3}+2$ units and their included angle is $60^{\circ}$,then the third side of the triangle is

In a $\triangle ABC$,the expression $(a-b)^2 \cos^2 \frac{C}{2} + (a+b)^2 \sin^2 \frac{C}{2}$ is equal to:

If the radius of the circumcircle of an isosceles triangle $PQR$ is equal to $PQ$ (where $PQ = PR$),then the angle $P$ is

In $\triangle ABC$,if $\tan \frac{A}{2}+\tan \frac{C}{2}=\frac{b}{s}$,then $\sin \left(\frac{A+C}{3}\right)=$

Consider a triangle $ABC$ and let $a, b$ and $c$ denote the lengths of the sides opposite to vertices $A, B$ and $C$ respectively. Suppose $a=6, b=10$ and the area of the triangle is $15 \sqrt{3}$. If $\angle ACB$ is obtuse and if $r$ denotes the radius of the incircle of the triangle,then $r^2$ is equal to

If $a^2, b^2, c^2$ are in $A.P.$,then which of the following are also in $A.P.$?