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Mathematical trajectory problem
1 The locus passing through the centers of two known points A and B is (line segment AB perpendicular bisector).

2 The locus of the vertex of an isosceles triangle with AB as the base is (from the middle perpendicular of the line segment AB to the midpoint).

3 The locus of vertex C of a right triangle with line segment AB as hypotenuse is (circle with diameter AB, go to point A and point B).

Analysis: 1. Let the centers of A and B be O, then OA=OB, and all points O, A and B defined by the circle are on the circle O with radius R, and OA=OB, so it can be judged that the trajectory of O is the perpendicular line of AB.

2. Let the vertex of the isosceles triangle be C, and similarly, the median vertical line of segment AB of C can be obtained. If ABC is a triangle, then C can't be on AB, and the trajectory of C can be taken as the middle vertical line (to the midpoint) of segment AB.

3. Because A, B and C are right triangles and AB is hypotenuse, then ∠ C = 90, then for point D of AB, there is DC=DA=DB, so A, B and C are on circle D, if the diameter of circle D is AB (straight lines A, B, D * * *, and C is not on AB (ABC is