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 \(AB\) at the points \(D\) (which does not coincide with \(C\)) and \(E\), respectively. Prove that \(AD < 2AE\).

Dots vienādsānu trijstūris \(ABC\), kuram \(AB=AC\) un \(\sphericalangle BAC < 60^{\circ}\). Rinķa līnija, kuras centrs ir punktā \(B\) un rādiuss \(BC\), krusto trijstūra malas \(AC\) un \(AB\) attiecīgi punktos \(D\) (kas nesakrīt ar \(C\)) un \(E\). Pierādīt, ka \(AD < 2AE\).