True or false? Prove it. I guess it would help to figure out whether 2 triangles can have the same circumcenter or orthocenter and not be congruent. I have no clue how to figure this out. If they aren't, then the nine-point circle would have to different. How would I go about solving this? Any help would be appreciated.
2026-04-28 15:25:05.1777389905
All triangles that have the same orthocenter and circumcircle have the same nine-point circle
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True. Let $H -$ orthocenter and $O -$ circumcenter, $R -$ radius, $F -$ midpoint $HO$. Then nine-point circle has a center point $F$ and a radius $\frac 12 R$