Question 151
Let $K$ and $L$ be the centers of excircles of a non-isosceles triangle $ABC$ lying opposite vertices $B$ and $C$, respectively. Let $B_1$ and $C_1$ be the midpoints of the sides $AC$ and $AB$, respectively. Let $M$ and $N$ be symmetric to $B$ and $C$ about $B_1$ and $C_1$, respectively.
Prove that the lines $MK$ and $LN$ meet the line $BC$ at the same point.
(D. Voinov)
Prove that the lines $MK$ and $LN$ meet the line $BC$ at the same point.
(D. Voinov)