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Math Help - 9 point circle, proportions of a bisected line

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    9 point circle, proportions of a bisected line

    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.)

    Thanks

    source of image:
    File:9pcircle 04.png - Wikipedia, the free encyclopedia
    Attached Thumbnails Attached Thumbnails 9 point circle, proportions of a bisected line-9pcircle_04-1-.png  
    Last edited by rainer; December 4th 2010 at 08:54 AM.
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