PQR is a triangle with its centroid at the point N and the circumcircle of PQR is denoted by L. The line segments PN, QN and RN meet L again respectively at the points S, T and U.

The respective lengths of the line segments PN, QN, RN, NS, NT and NU are denoted by a, b, c, d, e and f.

Determine (a/d + b/e + c/f).

using Geogebra geometry software I constructed the required segments for several different triangles and for all of them a=d b=e c=f  thus (a/d)+(b/e)+(c/f)=3

Posted by Daniel on 2008-01-18 09:25:26