Post Number:#4 by Thamim Zahin » Fri Apr 21, 2017 1:37 am
Let the lines $\overleftrightarrow{FE}$ and $\overleftrightarrow{BC}$ intersect at $M$. and let the segment $\overline{FE}$ and $\overline{AD}$ intersect at $N$. And let take $\overleftrightarrow{AP}$ and $\overleftrightarrow{QR}$ meet at $P_{\infty}$.
Now we know that $(M,D;B,C)$ is harmonic. Take the pencil at $E$. We get $(N,D;H,A)$ is harmonic. Now take the pencil at $P$. We get $(Q,R;H,P_{\infty})$ is harmonic.
$Q.E.D$ $\blacksquare$
 Attachments

 1212.png (79.24 KiB) Viewed 219 times
I think we judge talent wrong. What do we see as talent? I think I have made the same mistake myself. We judge talent by the trophies on their showcases, the flamboyance the supremacy. We don't see things like determination, courage, discipline, temperament.