Dear Steve, dear Deoclecio,

I'm sorry for my sporadic presence on Hyacinthos, but

let me make a remark here...

In Hyacinthos message #10270, Steve Sigur translated:

>> A line D meets sides BC, CA, AB of a triangle in

>> M, N, P. If we call alpha, beta, gamma the

>> angles of the diagonals AM, BN, CP of the

>> complete quadrilateral made from D and the three

>> sides of ABC and by theta the angle D makes with

>> the Newton line of this quadrilateral, we have

>> the relation

>>

>> cot theta = cot alpha + etc.

The definition of alpha, beta, gamma is not really

clear here - what does "angles of the diagonals"

mean? But if alpha, beta, gamma are meant to be

the angles *between* the diagonals, i. e. the angles

of the triangle formed by the lines AM, BN, CP, then

the result cannot be true in this form. In fact, the

angles alpha, beta, gamma are all defined

*symmetrically* with respect to the four lines BC,

CA, AB and D of the complete quadrilateral

(BC, CA, AB, D), while the angle theta is defined

*asymmetrically*, since its definition involves the

line D. Hence, cot theta cannot be generally equal to

cot alpha + cot beta + cot gamma. So I believe there

must be an error in the problem.

Friendly,

Darij Grinberg