Dear Randy,

[RH]

>

> What about the de Longchamps line of the excentral triangle (line at infinity intercept = X(513), or the Gergonne line of the excentral triangle?

I found that the de Longchamps line of the excentral triangle passes through (points in the range X(1)-X(3514):

X(239)

X(514)

X(649)

X(1019)

X(1021)

X(3218)

I also found a point outside the range X(1)-X(3514):

X(4560)

That's because it was in my personal database before it was registered in ETC.

Special is too that this line is the perpendicular bisector of:

X(1276), X(1277).

The coefficients of this line are: (b+c : c+a : a+b).

Hmmm, that's pretty spectacular ....... such simple coefficients....

I could not find it in the list of central lines.

I could not find any ETC-points in the range X(1)-X(3514) on the Gergonne Line of the Excentral Triangle.

However these intersection points should lie on this line:

X40.X164 ^ X348.X1216 (= X241 Excentral Triangle)

X44.X513 ^ X89.X3423 (= X650 Excentral Triangle)

X3.X266 ^ X9.X363 ^ X165.X503 (= X1465 Excentral Triangle)

X84.X2484 ^ X508.X2036 ^ X566.X1433 (= X1638 Excentral Triangle)

I hope these intersection points were secure measurements.

Best regards,

Chris van Tienhoven