If the sides of a triangle are $6, 10$ and $14$,then the triangle is

In a triangle,the sum of lengths of two sides is $x$ and the product of the lengths of the same two sides is $y$. If $x^2 - c^2 = y$,where $c$ is the length of the third side of the triangle,then the circumradius of the triangle is

In a triangle $ABC$,with usual notations,if $3b = a + c$,then $\cot \frac{A}{2} \cdot \cot \frac{C}{2} = $

The lengths of the sides of a triangle are $13, 14, \text{ and } 15$. If $R$ and $r$ respectively denote the circumradius and inradius of this triangle,then $8R - r = $

In a $\triangle ABC$,$\angle C = 60^{\circ}$ and $\angle A = 75^{\circ}$. If $D$ is a point on $AC$ such that the area of $\triangle BAD$ is $\sqrt{3}$ times the area of $\triangle BCD$,then the measure of $\angle ABD$ is (in $^{\circ}$)

In a triangle $ABC$ with usual notations,if $3a = b + c$,then $\cot \frac{B}{2} \cdot \cot \frac{C}{2} =$