Let ABC be a triangle with ∠BAC=90∘. Let O be the circumcenter of the triangle ABC and Γ be the circumcircle of the triangle BOC. Suppose that Γ intersects the line segment AB at P different from B, and the line segment AC at Q different from C. Let ON be the diameter of the circle Γ. Prove that the quadrilateral APNQ is a parallelogram. geometrycircumcircleperpendicular bisectorgeometry proposed