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  "body": "\n## Statement\n\nLet $A$, $B$, $C$ and $D$ be distinct [[concyclic points|049DCJZ448]] of the Euclidean plane $\\mathbb{R}^2$. Let $\\measuredangle$ be the [[oriented angle|03YN70NK0Z]], with values in $\\mathbb{R} / 2\\pi\\mathbb{Z}$.\nThen\n$$2 \\, \\measuredangle ACB = 2 \\, \\measuredangle ADB.$$\nFor the unoriented angles: if $C$ and $D$ are on the same side of the line $AB$, then $\\angle ACB = \\angle ADB$. If they are on opposite sides, then $\\angle ACB + \\angle ADB = \\pi$.\n\n## Remarks\n\nThe statement follows from the [[inscribed angle theorem|0GA1V8NN8C]]: both sides are equal to the oriented angle $\\measuredangle AOB$ at the centre $O$.\nThe factor $2$ is necessary. It removes the difference of $\\pi$ between points on the two arcs.\nThe case of opposite sides says that the opposite angles of a convex cyclic quadrilateral add up to $\\pi$.\n\n## Explanations\n\n### L1 human\n\nA segment of a circle is the region between a chord $AB$ and one of its arcs. From every point of that arc, the chord $AB$ is seen under the same angle. From the other arc, it is seen under the supplementary angle.\n",
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