The problem considered in [4] and [3] is as follows: Given n red points and m green points on plane, how to find a pair of red-green points such that the distance between them is smallest. This problem can be expanded for 3 sets of colored points [5]: Given n red points, m green points and p blue points on plane, how to find a trio of red-green-blue points such that the diameter of them is smallest. The diameter of the trio of 3 colored points is defined as size of the longest edge of the triangle formed by those 3 points. This problem seems to be a fundamental problem, but it is still open. An heuristic algorithm for this problem can be found in [5]. For the case that the sets of the given points are infinity, for example, the set of points on a line, then the combinatorial algorithm does not work any more. In this paper, the author use geometric methods to solve the following problem: Given a triangle ABC, how to find a trio of points M, N and P lying on the side BC, C A and AB, respectively, such that the diameter of the triangle MNP is smallest.