1. Two points are different: there are two points A and B in the picture. The straight line L is located between points A and B. Take a point P on the straight line L to minimize the distance between PA and Pb. Q: Where is the position of P?

2. Two points on the same side: the general drinks horses. There are two points a and b in the picture. The straight line L is located on the other side of point A and point B. Take a point P on the straight line L to minimize the distance between PA and Pb. Q: Where is the position of P?

3. Two points on the same side: There are two points A and B in the figure, and the straight line L is located on the other side of the two points A and B. Take a point P on the straight line L to maximize the distance between | pa-Pb |. Q: Where is the position of P?

4. Two points on different sides: There are two points A and B in the figure, and the straight line L is located between them. Take a point P on the straight line L to maximize the distance between | PA-Pb |. Q: Where is the position of P?

Single angle

5. Make an angle ∠o, with point A within ∠o, and take two points, E and F, on both sides of the angle to minimize the perimeter of △AEF?

Two parallel straight lines

6. Make points A and B, which are located outside two straight lines. Take two points e and f on two straight lines to minimize AE+EF+FB.

7. Make points A and B, with point A in a straight line and point B in a straight line. Take two points e and f on two straight lines to minimize AE+EF+FB.

8. Make points A and B, which are located in a straight line. Take two points e and f on two straight lines to minimize AE+EF+FB.

other

9. As shown in the figure, point B is a moving point on a horizontal straight line, and point E is on another straight line. How to determine the position of point E and point B to minimize AE+EB?

10. Points A and B are located above the straight line, and points E and F are located on the straight line. If the length of EF is determined as a, how to determine the positions of e and f to minimize AE+BF?

1 1. Bridge location problem: make two parallel straight lines, one side is point A and the other side is point B. Now, take a point on each of the two straight lines as e and f, and find the position of e and f to minimize AE+EF+FB.

12. Let ∠AOB be 90, point A and point B lie on OA and OB, and let point C form a triangle with points A and B to find the maximum value of OA.

13. Make a circle O, and the point P is located outside the circle O. Find the nearest point and farthest point of the point P on the circle O respectively.