圆内接与外切三角形中的某些极值问题

Some Extreme Value Problems for Inscribed and Circumscribed Triangles in a Circle

求内接于定圆的最大面积的三角形 ,或求外切于定圆的最小面积的三角形这类极值问题 ,是初等几何中常常遇到 ,但用纯初等几何方法又无法解决的问题 ,在本文中 ,运用局部对称与迭代等方法 。

Some problems of extreme value of area of triangle which is inscribed or circumscribed a identical circle, are often seen in elementary geometry but can not be solved by the method of single elementary geometry. In this paper, by using locally symmetric or successive method and etc. these problems are readily solved.