Dear All My Friends,
I have found the proof for Centroid case and it is not too hard. It is based on wellknown fact that if P is on Feuerbach hyperbola or on line X(1)X(3) then the pedal circle of P contains Feuerbach point.
TaTbTc is pedal triangle of the point P with barycentrics:
a*(a*b*c - 3*a*SA - 2*(b + c)*sb*sc) : :
This point is on line X(1)X3 and X(1)P/PX(3) = 2
Search value: +5.085011432616 may be not in current ETC.
Best regards,
Bui Quang Tuan
I have found the proof for Centroid case and it is not too hard. It is based on wellknown fact that if P is on Feuerbach hyperbola or on line X(1)X(3) then the pedal circle of P contains Feuerbach point.
TaTbTc is pedal triangle of the point P with barycentrics:
a*(a*b*c - 3*a*SA - 2*(b + c)*sb*sc) : :
This point is on line X(1)X3 and X(1)P/PX(3) = 2
Search value: +5.085011432616 may be not in current ETC.
Best regards,
Bui Quang Tuan
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