A Brahmagupta quadrilateral is a cyclic quadrilateral that has integer side and diagonal lengths with an integer area. The authors prove that a Brahmagupta quadrilateral can be placed in the plane with its vertices having rational coordinates and thus integer ones by some rotation, see [\textit{J. Fricke}, ``On Heron simplices and integer embedding'', Preprint, \url{arXiv:math/0112239}]; an illustrated example is later given. The authors also prove (indirectly) Ptolemy's inequality by showing a trigonometric quadrilateral identity in the Theorem 2 proof.