Let $a, b$ and $c$ be the lengths of the sides of a triangle with its opposite angles $A, B$ and $C$ respectively. If $\angle C=60^{\circ}$,then the value of $\frac{c(a+b)+(a^2+b^2)}{(b+c)(c+a)}$ is

If the sides of a triangle are in the ratio $\sqrt{3} : \sqrt{5} : \sqrt{8+\sqrt{15}}$,then the largest angle in that triangle is

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:

The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Then the sides of the triangle are

The angles $A, B, C$ of a triangle $ABC$ are in $AP$. If $AB=6$ and $BC=7$,then $AC=$

In a $\triangle ABC$,if $\angle A = 3\angle B$,$CA = 9$,and $BC = 16$,then the length of $AB$ is