551. On one of the sides of triangle $A B C$ there is a point $P$; draw a line through $\boldsymbol{P}$ that cuts off from triangle $\boldsymbol{A} \boldsymbol{B} \boldsymbol{C}$ a triangle similar to it. How many solutions?
551. In general, there are 4 solutions. If the triangle is isosceles or equilateral, the number of solutions decreases accordingly.