Let $ ABC $ be a triangle, let $ O $ and $ \gamma $ be its circumcentre and circumcircle, respectively, and let $ P $ and $ Q $ be distinct points in the interior of $ \gamma $ such that $ O, P $ and $ Q $ are not collinear. Reflect $ O $ in the midpoint of the segment $ PQ $ to obtain $R,$ then reflect $R$ in the centre of the nine-point circle of the triangle $ABC$ to obtain $S.$ The circle through $P$ and $Q$ and orthogonal to $ \gamma , $ crosses the rays $OP$ and $OQ,$ emanating from $O,$ again at $P'$ and $Q'$ respectively. Let the lines $PQ'$ and $QP'$ cross at $T.$ Prove that, if $P$ and $Q$ are isogonally conjugate with respect to the triangle $ABC,$ then so are $S$ and $T.$ E.D. Camier