Don't study hard when you do the problem! Look at the picture below ...

What's the difference between these two line segments? A-x, of course

It is represented by a linear function.

y=a-x

For this function, when a is fixed, x is the minimum and y is the maximum. ...

Now let's construct another function.

t=a+x

Did x take the minimum value just now? For this function, what happens when x is minimum? T is the smallest!

So for any case where the subtraction between AB and BC is the largest, it is equivalent to asking whether the addition between AB and BC is the smallest. Did the teacher talk about the maximum value of addition when he talked about the problem? ! When one side remains the same and the other side will change, transform it!

Of course, if the moving point passes through the middle vertical line of two fixed points, please answer that the distance difference is at least 0 (the distance from any point of the middle vertical line to both ends of the line segment is equal).

For arbitrarily fixed AB and moving point O on the plane, pay attention to the maximum value of AOB*** line, and prove that it is greater than the difference between the two sides with the third side of the triangle. (in particular, it depends on who is older, ao.