The lengths of sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Then the length of the sides of the triangle (in units) are

If two angles of $$\triangle \mathrm{ABC}$$ are $$\frac{\pi}{4}$$ and $$\frac{\pi}{3}$$, then the ratio of the smallest and greatest sides are

In $$\triangle \mathrm{ABC}, \mathrm{m} \angle \mathrm{B}=\frac{\pi}{3}$$ and $$\mathrm{m} \angle \mathrm{C}=\frac{\pi}{4}$$. Let point $$\mathrm{D}$$ divide $$\mathrm{BC}$$ internally in the ratio $$1: 3$$, then $$\frac{\sin (\angle B A D)}{\sin (\angle C A D)}$$ has the value

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 $$x^2-\mathrm{c}^2=y$$, where $$\mathrm{c}$$ is the length of the third side of the triangle, then the circumradius of the triangle is