15.0 Ptolemy's Theorem

  Complex Numbers

    15.0 Ptolemy's Theorem

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15.0 Ptolemy's TheoremIt states that the product of the lengths of the diagonals of a convex quadrilateral inscribed in a circle is equal to the sum of the products of lengths of the two pairs of its opposite sides i.e., $AC.BD$=$AB.CD+AD.BC$ or $$\left| {{z_1} - {z_3}} \right|\left| {{z_2} - {z_4}} \right| = \left| {{z_1} - {z_2}} \right|\left| {{z_3} - {z_4}} \right| + \left| {{z_1} - {z_4}} \right|\left| {{z_2} - {z_3}} \right|$$