Butterfly Effect

Geometry Level 5

The lines above are drawn joining points \(A, B, D, E\) on the circumference of the circle, such that \(BD\) is a diameter of \(20\) and \(\angle ABC = 2\angle BAC.\)

If \(AC = 3\), what's the ratio of the areas of the two triangles, blue \(\triangle CDE\) to red \(\triangle ABC?\)

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