In the acute triangle ABC, the altitude AH is drawn. Using segments AB,BH,CH and AC as diameters circles ω1,ω2,ω3 and ω4 are constructed respectively. Besides the point H, the circles ω1 and ω3 intersect at the point P, and the circles ω2 and ω4 interext at point Q. The lines BQ and CP intersect at point N. Prove that this point lies on the midline of triangle ABC, which is parallel to BC. midlinegeometrycirclesUkrainian TYM