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  "body": "\n## Definition\n\nLet $ABCD$ be a quadrilateral in the Euclidean plane $\\mathbb{R}^2$, with the vertices $A$, $B$, $C$, $D$ in this order.\nThe quadrilateral $ABCD$ is cyclic if its four vertices are [[concyclic|049DCJZ448]]. The circle through them is its [[circumcircle|03VZJE6C8C]].\n\n## Remarks\n\nA convex quadrilateral $ABCD$ is cyclic if and only if its opposite angles add up to $\\pi$: $\\angle DAB + \\angle BCD = \\pi$. The direct part is Proposition 22 of Book III of Euclid's Elements.\nEach rectangle is cyclic. A rhombus that is not a square is not cyclic.\nUsually the quadrilateral is taken to be convex. A crossed quadrilateral with concyclic vertices is a crossed cyclic quadrilateral.\n\n## Explanations\n\n### L1 human\n\nEach triangle fits in a circle, but a quadrilateral does not always. A quadrilateral is cyclic when one circle passes through all four corners. A simple test: the angles at two opposite corners add up to a straight angle.\n",
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