86年江苏省初中数学竞赛第五题: 在平面上任意给定5个点,其中任何三点不在一条直线上,并且它们不是凸五边形的顶点,证明下列两个结论中必有一个成立: (1)存在以某四点为顶点的凸四边形,而另一点在该四边形内; The 86th Jiangsu Provincial Junior High School Mathematical Contest in Question 5: Given 5 points arbitrarily on the plane, any three of them are not on a straight line, and they are not the vertices of the convex pentagon. Proof that one of the following two conclusions is true : (1) There is a convex quadrangle with some four points as the vertices, and another point is within the quadrilateral;