Let O be the circumcenter of the triangle ABC. The segment XY is the diameter of the circumcircle perpendicular to BC and it meets BC at M. The point X is closer to M than Y and Z is the point on MY such that MZ=MX. The point W is the midpoint of AZ.
a) Show that W lies on the circle through the midpoints of the sides of ABC;
b) Show that MW is perpendicular to AY. geometrycircumcirclevectorgeometric transformationhomothetyratiotrapezoid