Hu Bugui problem is a weighted line segment and maximum problem (line segment with coefficient and maximum problem), which is a very old mathematical problem and was once a very famous "difficult problem" in history. Its typical feature is to find the form of AP+kBP.

The maximum value of "PA+K Pb" is a hot topic in senior high school entrance examination. This kind of problem is usually classified according to the different images where the moving point P is located. The type of point P moving in a straight line is called "Hu Bugui" problem, and the type of point P moving in a circle is called "Arrhenius circle" problem.