Question 161
Let $ABC$ be an acute triangle, and let $D$, $E$, $F$ be the feet of its altitudes from $A$, $B$, $C$, respectively. The lines $AB$ and $DE$ cross at $K$ and the lines $AC$ and $DF$ cross at $L$. Let $M$ be the midpoint of the side $BC$ and let the line $AM$ cross the circle $ABC$ again at $N$. Finally, the parallel through $M$ to $EF$ crosses the line $KL$ at $P$. Show that the triangle $MNP$ is isosceles.
Andrei Bâra
Andrei Bâra