A Line Through the Circumenter.

Any line through the circumcenter intersects the circumcircle in two antipodal points Q and Q'. This line intersects the sides in points X, Y and Z. Circles with diameters from these points to the opposite vertex are constructed. These three circles intersect at points T on the circumcircle and W on the nine-point circle. Point W is the point where the two orthogonal Simson lines of Q and Q' intersect. The line through T and W pass through the orthocenter H. Use the tools to confirm both of these claims.