关于已知△ABC 的三边 a、b、c 求△ABC的面积 S_△、外接圆半径 R、内切圆半径 r,是在解三角形以及立体几何中涉及较多的计算问题.如果注意探索相关元素之间的内在联系,不难提炼出一种行之有效的套路解法.本文给出这一解题套路(简称“连环套”法):先由余弦定理求出 cosx(x 是△ABC 中任意一个角),从而推出 sinx,再由正弦定理求 R,由 S_△=1/2absinC,求 S_△,又由 S_△=1/2r(a+b+c)求 About the known three sides a, b, c of △ABC, the area S_△, the circumscribed circle radius R, and the inscribed circle radius r of △ABC are more computational problems involved in solving triangles and solid geometry. The intrinsic relationship between related elements is not difficult to extract an effective solution. This paper presents this problem solving set (abbreviated as “linked sets” method): first by the cosine theorem cosx (x is △ABC in any angle), thus the introduction of sinx, and then by the sine theorem to find R, by S_△=1/2absinC, find S_△, and by S_△=1/2r(a+b+c) seeking