Problem B. 4654. (October 2014)

B. 4654. In a triangle \(\displaystyle ABC\), let \(\displaystyle AD\) be an altitude, let \(\displaystyle BE\) be an angle bisector, and let \(\displaystyle CF\) be a median. Prove that the lines \(\displaystyle AD\), \(\displaystyle BE\) and \(\displaystyle CF\) are concurrent exactly if \(\displaystyle ED\) is parallel to \(\displaystyle AB\).

(4 pont)

Deadline expired on November 10, 2014.

Statistics:

161 students sent a solution.
4 points:	77 students.
3 points:	30 students.
2 points:	37 students.
1 point:	14 students.
0 point:	3 students.

Problems in Mathematics of KöMaL, October 2014