id: 06408326
dt: j
an: 2015b.00685
au: Stephenson, Paul
ti: Cyclicity.
so: Math. Sch. (Leicester) 39, No. 4, 34-35 (2010).
py: 2010
pu: Mathematical Association (MA), Leicester
la: EN
cc: G40
ut: cyclic quadrilaterals; incyclic polygons; cyclic $2n$-gons; circumcircles;
hexagons; supplementary angles; alternate angles; proofs; elementary
geometry; generalisation; solid geometry; hexahedrons; spheres
ci:
li:
ab: 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.
rv: