Problem 190

Given the ABC triangle parallel one draws up one to AB so that it divides the perimeter by half.

One draws up other parallel lines to BC and CA with the same condition.

These three parallel lines conform the triangle MNP.

To prove:

a) MNP is homothetic to ABC.

b) Study the homothetic center, U, in the ETC of Clark Kimberling.

That is to say, to find with ten decimals "height" of U on the triangle of sides 6 cm (horizontal) 9 cm (straight) 13 cm (left) of Clark Kimberling, and to catalogue it between its 2445 points of the triangle.

Barroso, R. (2004). Personal communication. (With permission of Clark Kimberling, to whom I thank for his gentility)

Traducción de María Barroso Tristán, estudiante de Filología Inglesa en la Universidad de Sevilla