Appearances are sometimes deceiving

Geometry Level 3

A triangle's angles are: \(40°\), \(60°\), and \(80°\). We drop perpendiculars from the midpoints of the sides as is shown the figure below.

If the area of the blue hexagon is \(t\), and the area of the triangle is \(T\), then find the value of \(\dfrac{t}{T}\).

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