\input zb-basic \input zb-matheduc \iteman{ZMATH 2015b.00685} \itemau{Stephenson, Paul} \itemti{Cyclicity.} \itemso{Math. Sch. (Leicester) 39, No. 4, 34-35 (2010).} \itemab From the text: This piece is about generalizing theorems and their converses (or trying to), picking up the theme from earlier issues of this journal. Among the NRICH problems for March 2009 was `Cyclic quad jigsaw'. You were told that the constituent quadrilaterals in this figure were cyclic and asked to show that the outline was too. If you haven't already met this one, try it. All the facts you need are that the angles around a point sum to a whole angle, that the opposite angles of a cyclic quadrilateral are supplementary and that the converse is true: a quadrilateral whose opposite angles are supplementary is cyclic. \itemrv{~} \itemcc{G40} \itemut{cyclic quadrilaterals; incyclic polygons; cyclic $2n$-gons; circumcircles; hexagons; supplementary angles; alternate angles; proofs; elementary geometry; generalisation; solid geometry; hexahedrons; spheres} \itemli{} \end