Let Ea, Eb, Ec be the excenters, P
a point. Let Aa, Ab, Ac be the orthogonal projections of A on AP, BP, CP
and Oa the circumcenter of AaAbAc. Define analogously Ob, Oc. The ninecenter
Np of OaObOc lies in the Euler line. When P is the orthocenter H, the triangles
ABC, OaObOc have the same ninecircle.
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