In a less “higher” maths fashion : This Numberphile video somewhat says that Pythagoras theorem is a special case of Ptolemy’s theorem which is a more general view of properties of a cyclic quadrilateral. But navigating between the 2 always seems some sort of tautology to me …
There is also Casey’s theorem which reduces to Ptolemy’s (so which could reduce to Pythagoras’).
Quoting the Ptolemy’s theorem Wikipedia article :
More generally, if the quadrilateral is a rectangle with sides $a$ and $b$ and diagonal $d$ then Ptolemy's theorem reduces to the Pythagorean theorem. In this case the center of the circle coincides with the point of intersection of the diagonals. The product of the diagonals is then $d^2$, the right hand side of Ptolemy's relation is the sum $a^2 + b^2$.
Later on, it is cited as a corollary theorem.
