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

Let $ABC$ be a triangle such that $AB=15$ and $AC=9$. The bisector of $\angle BAC$ meets $BC$ in $D$. If $\angle ACB=2\angle ABC$,then $BD$ is

In $\triangle ABC$,if $a: b: c = 3: 5: 7$,then $\cos A + \cos B =$

With usual notations,in any $\triangle ABC$,if $a \cos B = b \cos A$,then the triangle is:

In $\triangle ABC$,if $(r_2-r_1)(r_3-r_1)=2 r_2 r_3$,then $2(r+R)=$

Let $ABC$ be a triangle with $\angle C=90^{\circ}$. Draw $CD$ perpendicular to $AB$. Choose points $M$ and $N$ on sides $AC$ and $BC$ respectively such that $DM$ is parallel to $BC$ and $DN$ is parallel to $AC$. If $DM=5$ and $DN=4$,then $AC$ and $BC$ are respectively equal to: