Geometry
# Inscribed and Circumscribed Figures

A circle is inscribed in a hexagon, as shown in the diagram.

Is it possible that the side lengths of the hexagon are \[7,9,11,13,15,17\] in some order?

In the figure, each of the three circles is tangent to the other two and each side of the equilateral triangle is tangent to two of the circles.

If the length of one side of the triangle is 4, what is the radius of each circle?

**Details and assumptions**:

\(\bullet\) All the three circles have equal radii.

The area of the largest region can be written as \( A \pi \). What is \(A \)?

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