Given the triangle, 9-point circle, and circumcircle shown in the attached image (borrowed from wikipedia):
If we designate the point where the line beginning at T3 reaches the other side of the circumcircle as "X," and T3X passes through the triangle orthocenter S as shown, and the length of T3X is known, is there anyway to derive from that knowledge (and from the properties of the 9-point circle) the lengths of SX or ST3?
(EDIT: Note that T3F=FS and SX is likewise bisected by the 9 point circle.)
source of image:
File:9pcircle 04.png - Wikipedia, the free encyclopedia