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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.
1
vote
Thales' semicircle theorem in higher dimensions
This ia modest, marginally on topic comment which I am adding in the hope that it might be of assistance. The OP interprets the Thales theorem as identifying the locus of points in a plane at which a …
0
votes
Can Morley's theorem be generalized?
Possibly not what you are looking for but it does correspond to the question raised in the title. One can determine those auxiliary triangles $A_1B_1C_1$ of $ABC$ which are equilateral in terms of th …