  The inscribed angle theorem, a famous result about the angle subtended by a
chord within a circle, is well known and commonly taught in school curricula.
In this paper, we present a generalisation of this result (and other related
circle theorems) to the rectangular hyperbola. The notion of angle is replaced
by pseudo-angle, defined via the Minkowski inner product. Indeed, in Minkowski
space, the unit hyperbola is the set of points a unit metric distance from the
origin, analogous to the Euclidean unit circle. While this is a result of pure
geometrical interest, the connection to Minkowski space allows an
interpretation in terms of special relativity where, in the limit $c\to\infty$,
it leads to a familiar result from non-relativistic dynamics. This
non-relativistic result can be interpreted as an inscribed angle theorem for
the parabola, which we show can also be obtained from the Euclidean inscribed
angle theorem by taking the limit of a family of ellipses ananlogous to the
non-relativistic limit $c\to\infty$. This simple result could be used as a
pedagogical example to consolidate understanding of pseudo-angles in
non-Euclidean spaces or to demonstrate the power of analytic continuation.
