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ABCDEF is an equiangular hexagon. Points A1, B1, C1, D1, E1, F1 are the intersection points of extensions of several pairs of the sides of ABCDEF. If the perimeter of hexagon ABCDEF is 15, what is the smallest perimeter of dodecagon 

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 Jan 17, 2020
 #1
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The smallest perimeter is 20.

 Jan 18, 2020
 #2
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The number of degrees in the interior angles of a hexagon is 720°.

Since the hexagon is equiangular, each interior angle is 120°.

Therefore, each exterior angle of the hexagon is 60°.

This means that each one of the exterior triangles created on the hexagon is an equilateral triangle.

The sum of the two exterior sides of each triangle is equal to twice the length of the side of the hexagon.

Since the perimeter of the hexagon is 15, the sum of the sides created on the exterior of the hexagon is twice this, or 30.

 Jan 18, 2020

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