A Line Through the Circumenter.
- Author:
- Steve Phelps
- Topic:
- Geometry
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.