In a triangle $$ABC$$, let $$\angle C = {\pi \over 2}$$. If $$r$$ is the inradius and $$R$$ is the circumradius of the triangle, then $$2(r+R)$$ is equal to

In a triangle $$ABC$$, $$2ac\,\sin {1 \over 2}\left( {A - B + C} \right) = $$

Let $${A_0}{A_1}{A_2}{A_3}{A_4}{A_5}$$ be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments $${A_0}{A_1},{A_0}{A_2}$$ and $${A_0}{A_4}$$ is

If in a triangle $$PQR$$, $$\sin P,\sin Q,\sin R$$ are in $$A.P.,$$ then