PS

The foregoing lays the groundwork for a proof of the "Angle at the centre" theorem. It's an elegant alternative to the familar approach involving isosceles triangles.
[See: Mathematics in School, March 2005, 34, 2, page 13.]

The above variant takes a more general view and points towards the "Angles in the same segment" theorem. If we think of points R and P as fixed in the diagram above, but vary the position of Q (and hence of S and T), then arc QST will always be the same size, as will angle TPQ, yet P's position relative to arc QST will vary.

The end

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