三角形中的不等式问题,也就是边与边、角与角、边角之间以及边、角、面积、内切圆半径、外接圆半径……之间的不等量关系问题。其中三边之间、三角之间基本的等量关系及不等量关系又是证明这类问题的基础。如两边之和大于第三边;两边之差小于第三边;任何一边均小于周长之半:三角中至少有一个角小于60°;大边对大角、大角对大边以及锐角三角形中任意两边的平方和均大于第三边的平方等等。此外,还有一些常用的基本不等式也是证明这类问题 The problem of inequality in triangles is the problem of unequal relations between edges and edges, corners and corners, corners, and edges, corners, areas, inscribed circle radii, circumcircle radii, and so on. The basic equal relations between the three sides and triangles and the unequal relations are the basis for proving such problems. If the sum of the two sides is greater than the third side; the difference between the two sides is smaller than the third side; either side is less than half of the perimeter: at least one corner in the triangle is less than 60°; the large side is opposite to the big corner, the large corner to the large side, and any two sides of the acute triangle. The sum of squares is greater than the square of the third side, and so on. In addition, there are some common basic inequalities that also prove this kind of problem