The concept of inverse triangles is introduced in $ETC$ in the preamble above X(42005), by Clark Kimberling and Peter Moses, where we can find the cases of cevian and anticevian triangles.
Circumcevian triangles and their inverses are treated in the preamble just before X(43344).
However a construction of these triangles is missing at the moment.
PDF: A construction of the inverse of circumcevian triangles
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