So first of all, just incase you don't know, Feuerbach's Theorem states the nine-point circle of a triangle in Euclidean space is tangent to the three excircles and the incircle of the triangle. However, does this theorem hold for spherical triangles? Because it seems like you can't have tangent sides of a triangle to a circle on a spherical surface? If so, can another theorem be found with a similar relation besides tangency?
2026-03-26 01:01:12.1774486872
Feuerbach's Theorem in Spherical Triangle?
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