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

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

Let $$f\left( x \right) = \left\{ {\matrix{ {\left| x \right|,} & {for} & {0 < \left| x \right| \le 2} \cr {1,} & {for} & {x = 0} \cr } } \right.$$ then at $$x=0$$, $$f$$ has

For all $$x \in \left( {0,1} \right)$$