Knowing \(ω\)

Geometry Level 4

Let \(A, B, C, D\) (written in the order from left to right) be four equally-spaced collinear points. Let \( ω\) and \(ω^{'}\) be the circles with diameters \(AD\) and \(BD\), respectively. A line through \(A\) that is tangent to \(ω^{'}\) intersects \(ω\) again at point \(E\). If \(AB=2\sqrt{3}\) cm, what is \(AE\) (in centimeters)?

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