9967New property of X(1358) + a new related point
- Jul 1, 2004Dear Hyacinthians,
X(1358) is defined in the current ETC as the Brisse-transform
I would like to present a new remarkable property of this point
Let A'B'C' be the medial triangle of triangle ABC.
Consider the circle, different from the ninepointcircle, through B'
and C' touching the incircle. Let A* be the point where both circles
touch. Define B* and C* similarly.
X(1358) is the perspector of the triangles ABC and A*B*C*
Its barycentrics are ( (b-c)^2/(b+c-a) : cyclic.....)
If we replace the medial triangle by the orthic triangle we get a
new point S with similar barycentrics
S = ( (b-c)^2.(b+c-a)^3 : cyclic.....)
Greetings from Bruges
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