Forum Geometricorum, 10 (2010) 99--107.

Abstract: We study three problems concerning the determination of the maximal cyclic quadrangle under certain restrictions on its diagonals: (a) assuming that one of the diagonals as well as the intersection point of the two diagonals are fixed, (b) assuming that the location of the intersection point of the two diagonals is fixed, and (c) assuming that the intersection point of the diagonals is fixed and the diagonals intersect under a constant angle.

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