Inscribed Ellipse in a Parallelogram

Geometry Level 3

Parallelogram $$ABCD$$ with $$AB = 10, BC =16, \angle ABC = 60^{\circ}$$ has an inscribed ellipse such that the tangent point $$E$$ satisfies $$CE = \frac{3}{4} CD$$.

Find the length of the semi-major axis of this ellipse.

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