Given an isosceles triangle \(ABC\) with \(AB = AC\) and \(\sphericalangle BAC<60^{\circ}\). The circle with center at point \(B\) and radius \(BC\) intersects the sides \(AC\) and \(AB\) of the triangle at points \(D\) and \(E\), respectively. Compute \(\frac{AD}{DC}\) if \(\frac{AE}{EB}=\frac{2}{5}\).

Dots vienādsānu trijstūris \(ABC\), kuram \(AB = AC\) un \(\sphericalangle BAC<60^{\circ}\). Riņka līnija, kuras centrs ir punktā \(B\) un rādiuss \(BC\), krusto trijstūra malas \(AC\) un \(AB\) attiecīgi punktos \(D\) un \(E\). Aprēķināt \(\frac{AD}{DC}\), ja \(\frac{AE}{EB}=\frac{2}{5}\).