Consider a semicircle of radius 1 on the diameter \(AB\) where the center is \(O\).

A point \(C\) divides \(AO \) in the ratio \(2:1\).

A line that is perpendicular to \(AO \) passing through \(C\) cuts the semicircle at \(E\).

Another line \(OL\) passing through \(O \) and is perpendicular to \(AE\) intersects \(CE\) at \(H\).

Find the value of \(EH\).

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