Let's take a look at these three interesting maximum problems. The first is the maximum value of a moving point on a circle. We need to separate this point from the circle to discuss it, and the coordinates of this point are known. Convert it into the formula of the distance from the outer point of the circle to the center of the circle, and the radius of addition and subtraction is as shown in figure 1; ?
When the fixed point outside the circle becomes an infinite number of points (points move into lines), it becomes the second problem: the maximum value of the fixed point on the line and the circle. Obviously, this straight line is worth discussing only if it is out of the circle. The idea of solving the problem of the maximum value between the first point outside the circle and the circle can be further transformed into the distance between the center of the circle and the straight line, as shown in Figure 2. ?
When a straight line outside the circle (a straight line separated from the circle) is bent into a circle, and there is no intersection between the two circles (separated from each other), the third problem arises: the distance between the moving point on the circle and the moving point on the circle, or whether you keep pressing the center of the circle and keep the radius unchanged, and further convert it into center distance plus two radii or center distance minus two radii (center distance refers to the distance between two centers), as shown in Figure 3?
With the solutions of the above three modes. The key is to see how to transform when encountering problems. It is the most valuable question not to tell us as soon as it comes up. This depends on our excavation and analysis of known topics. It's better to practice it once than to say it a hundred times. Practice is the only criterion for testing truth.