Let $N$ be the point inside a rhombus $ABCD$ such that the triangle $BNC$ is equilateral. The bisector of $\angle ABN$ meets the diagonal $AC$ at $K$. Show that $BK=KN+ND$.
Source: Ukraine 1999 Grade 8 P5
Tags: geometry, rhombus
Let $N$ be the point inside a rhombus $ABCD$ such that the triangle $BNC$ is equilateral. The bisector of $\angle ABN$ meets the diagonal $AC$ at $K$. Show that $BK=KN+ND$.