问题:已知⊙O_1的半径为3,⊙O_2的半径为1,圆心距为7,求与⊙O_1外切且与⊙O_2内切的⊙O的半径。 对于此题,绝大部分学生都会作出如图1所示的图形,从而得出所求⊙O的半径为2.5。 现在的问题是与⊙O_1外切的点A和与⊙O_2内切的点B是否与O_1、O_2共线?上述的解答默认O_1、A、O_2、B四点共线。由两圆相切 Problem: It is known that ⊙O_1 has a radius of 3, ⊙O_2 has a radius of 1, and the center distance is 7. Find the radius of ⊙O that is circumscribed with ⊙O_1 and ⊙O_2. For this question, the vast majority of students will make the graph shown in Figure 1, so that the radius of the ⊙O is 2.5. The question now is whether the point A with which ⊙O_1 is circumscribed and the point B with which ⊙O_2 is inscribed are collinear with O_1, O_2. The above-mentioned solution defaults to four lines of O_1, A, O_2, and B. Tangent from two circles