Theorem1.Let∆ABCbeatriangle. Theorthocenter,the centroid,the circumcenter,andthe nine-pointcenterof∆ABCarecollinear.Futher,Uis the
midpointofthe segmentHOandGlies onHOtwo-thirdsofthe distancefrom
Hto O.
Proof.Let∆ABCbeatriangle. First,weconstructthefourpointsinquestion.