  In this article we present a remarkable concyclicity of four centroids
related to the orthocenters of the triangles $ABC,$ $BPC,$ $CPA,$ and $PAB$ of
a quadrangle $ABCP$. Furthermore, we establish a result about orthologic
triangles inscribed in a rectangular hyperbola. We present an application of
the concyclic centroids theorem when $P$ corresponds to the incenter $I$ of
$ABC$. This specialization leads to the discovery of a novel triangle
intimately connected to the Fuhrmann triangle.
