8.41*. Given a triangle $A B C$, where $A B < B C$. Construct a point $D$ on the side $A C$ such that the perimeter of triangle $A B D$ is equal to the length of side $B C$.
8.41. Let's construct point $K$ on side $A C$ such that $A K = B C - A B$. Let point $D$ lie on segment $A C$. The equality $A D + B D + A B = B C$ is equivalent to the equality $A D + B D = A K$. For point $D$ lying on segment $A K$, the latter equality can be rewritten as $A D + B D = A D + D K$, and for point $D$ not lying on segment $A K$, it can be rewritten as $A D + B D = A D - D K$. In the first case, $B D = D K$, and the second case is impossible. Therefore, point $D$ is the intersection of the perpendicular bisector of segment $B K$ and segment $A C$.