A', B', C' the orthogonal projections of A, B, C on L, resp.

Let A*, B*, C* be points on AA', BB', CC', resp. such that:

A*A / A*A' = B*B / B*B' = C*C / C*C' = t

The triangles ABC, A*B*C* share the same centroid.

As t caries, which are the loci of O, H .... of A*B*C* ?

Special Case: L = the Euler Line

APH