# 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)?

×