1题目如图1，已知两个半径不等的圆O1与圆O2相交于M、N两点，且圆O1与圆O2内切于S、T两点，求证：OM上MN的充要条件是S、N、T三点共线（满分50分，命题组供题）这是1997年全国高中联赛第二试中第一大题，命题组为改卷提供的参考答案只有一种证法【’］．其实，平面几何问题，常 The 1 problem is shown in Fig. 1. Two circles O1 with different radii are known to intersect with circle O2 at two points M and N, and circle O1 and circle O2 are cut at two points S and T. Proof: The charge of MN on OM is sufficient. The conditions are S, N, and T. The three points are collinear (out of 50 points, the subject is for questions). This is the first major question in the second national high school league trial in 1997, and there is only one kind of reference answer for the proposition group. law【’]. In fact, plane geometry problems, often