# 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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