Inside the acute-angled triangle ABC we take P and Q two isogonal conjugate points. The perpendicular lines on the interior angle-bisector of ∠BAC passing through P and Q intersect the segments AC and AB at the points Bp∈AC, Bq∈AC, Cp∈AB and Cq∈AB, respectively. Let W be the midpoint of the arc BAC of the circle (ABC). The line WP intersects the circle (ABC) again at P1 and the line WQ intersects the circle (ABC) again at Q1. Prove that the points P1, Q1, Bp, Bq, Cp and Cq lie on a circle.Proposed by P. Bibikov geometryisogonal conjugatesKvant