Incircle of a polygon
A polygon has exactly one side which lenght is
, the other sides' lenght are
.
Is it possible to write an incircle to the polygon?
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1 solution
Let's assume that it is possible. Then the side size 2 will, due to symmetry, be tangent the circle in the middle the side. That means the distance from the point of contact to the vertex will be 1. If we then take a side size 1 and continue from that vertex and make this side tangent to the circle, as required if there is an incircle, the other end of the side will end on the circle. But that is not a possible location of a vertex, if the next side too is to be tangent to the same circle. It is therefore not possible for a polygon to have all sides except one size 1, the remaining side size 2, and have an inscribed circle.