Angle Divider Theorem for a Cyclic Quadrilateral
For a proof of the quadrilateral case, read my AMESA 1996 paper An interesting Side-Angle Duality in Geometry.
For a side-angle dual of this result involving the side dividers of a circumscribed/tangential quadrilateral go to Side Divider Theorem for a Circumscribed Quadrilateral.
For dynamic versions of the Angle & Side Divider cases for a Triangle go to Conway's Circle Theorem as special case of Side Divider Theorem.
Proofs of this result, its dual & of the generalizations, are given in Some Adventures in Euclidean Geometry as well as generalizations to cyclic polygons with an even or odd number of sides. My book is now available for free to download as a PDF at Some Adventures in Euclidean Geometry.
Related Links
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Updated by Michael de Villiers, 24 March 2012; updated 3 September 2020 with WebSketchpad; uodated 13 March 2025.