Let ABC be an acute triangle with AB<AC<BC,c it's circumscribed circle and D,E be the midpoints of AB,AC respectively. With diameters the sides AB,AC, we draw semicircles, outer of the triangle, which are intersected by line D at points M and N respectively. Lines MB and NC intersect the circumscribed circle at points T,S respectively. Lines MB and NC intersect at point H. Prove that:
a) point H lies on the circumcircle of triangle AMN
b) lines AH and TS are perpedicular and their intersection, let it be Z, is the circimcenter of triangle AMN geometrycircumcirclesemicircleCircumcenter