Abstract:
Heron's well-known formula expressing the area of a triangle in terms
of the lengths of its sides is generalized in the following sense to polygons
inscribed in a circle: it is proved that the area is an algebraic
function of the lengths of the edges of the polygon. Similar results are
proved for the diagonals and the radius of the circumscribed circle.
The resulting algebraic equations are studied and elementary
geometric applications of the algebraic results obtained are presented.
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