Easy but Thought-ProvokingGeometry Level 3
In the diagram, point \(A\) outside a circle with center \(O\).
Draw tangents \(AB, AC\) to the circle, and line \(ADE\) intersects \((O)\) at \(D, E\) such that, \(BE\) and \(AC\) are parallel.
\(BD\) intersects \(AC\) at \(I\).
Let \(S\) be the point on \(AO\) such that \(BSIA\) (the yellow quadrilateral) is concylic.