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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 points)

Deadline expired on 10 November 2014.

Statistics on problem B. 4654.
 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

•  Támogatóink: Morgan Stanley