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We will state and prove a general theorem about shortest route through the periphery of a standard convex polygon.. We start with few definitions.
Standard convex Polygon: A standard convex polygon or SCP for short is one in which all the internal angles are between 900and 1800. A peculiar property of SCP is that all diagonals are greater than the two sides forming it, or adjacent sides to it. It is easy to establish since in a right triangle hypotenuse is diagonal or greatest side and as the opposite angle grows the diagonal side dilates. So if one angle is larger than 900 then one side i.e. side opposite to the before said angle is the largest side.
Now we are in a position to state our former result.
For all points lying on the periphery of a SCP, the shortest route between them is through the peripheral path.
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