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A geometry theorem

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Phil Todd



H1,H2 and H3 are feet of altitudes, M1,M2,M3 are midpoints. H is the orthocenter.  X2,X3,Y1,Y3,Z1,Z2 are formed by reflecting H1,H2 and H3 in the other altitudes.  X,Y,Z are the intersections between the lines joining midpoints to these reflected points.

Observe that H appears to be the incenter of XYZ so long as ABC is acute angled.

Otherwise it appears to be one of the excenters

Tags: orthocenter, incenter
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