Prove that the area \(S_{ABC}\) of a triangle is equal to \(abc/4R\).
The point \(D\) lies on the base \(AC\) of the isosceles triangle \(ABC\). Prove that the radii of the circumscribed circles of the triangles \(ABD\) and \(CBD\) are equal.
Express the area of the triangle \(ABC\) through the length of the side \(BC\) and the angles \(B\) and \(C\).