Question 51
Let $ABC$ be a triangle with $|AB| \gt |AC|$. Let $D$ be the foot of the altitude drawn from $A$ to $BC$, $K$ be the intersection of $AD$ and the internal bisector of the angle at $B$, $M$ be the foot of the perpendicular drawn from $B$ to $CK$ and $N$ be the intersection of $BM$ and $AK$. Let $T$ be the intersection of $AC$ with the line which passes through $N$ and is parallel to $DM$.
Show that $BM$ is the internal bisector of the angle $\angle TBC$.
Show that $BM$ is the internal bisector of the angle $\angle TBC$.