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Given any angle ABC
Centre the vertex draw an arc to cut the two arms: AB in P BC in S
Centre P and radius = PS draw a long seeking arc.
Centre S and radius PS, draw a defining arc to cut the arc centre P inD
BD will cut PS at its mid point, E
Centre E and radius EP draw a semi circle to cut PS at P and S.
Centre P and radius EP draw an arc to cut the semi circle centre E at Q
Centre S draw an arc radius ES, to cut the semicircle centre E at R
Join BQ, BR these lines will trisect thew circle.
The development of this technique rests on the extension of the Basic circle equality: equal chords in the same circle subtend equal angles at the circumference.
Given three equal adjacnt angles from the centre of a circle, then the subtending arcs will subtend three equal adjacent angle at any point on any concentric circle.
My paper which is being stolidly ignored by academia, (is in fact copyright) and contains euclidean style proofs leading up to and including the new equal angles proposition. I am willing to share the entire paper with anyone hwo promises to honour the copyright.