Derivation / Proof of Ptolemy's Theorem for Cyclic Quadrilateral

Ptolemy's theorem for cyclic quadrilateral states that the product of the diagonals is equal to the sum of the products of opposite sides. From the figure below, Ptolemy's theorem can be written as

$d_1 d_2 = ac + bd$


The Polygon

Polygon is a closed plane figure bounded by straight lines. There are two basic types of polygons, a convex and a concave polygon. Polygon is said to be convex if no side when extended will pass inside the polygon, otherwise it is concave.



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