Easy but Thought-Provoking

Geometry 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.

Find \(\dfrac{SA}{SO}\).


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