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文[1]借助两个特殊不等式并应用代数变换证明了一类三角形不等式.本文给出这类不等式的三角证法.为行文方便,约定△ABC的三边长、半周长、外接圆半径、内切圆半径分别为a、b、c、,s,R,r;其中例题的证明要用到下列熟知的三角形恒等式:abc=4Rrs,∑bc=s2+4Rr+r2,∑a2=2(s2-4Rr-r2)
The paper [1] proves a class of triangular inequalities by means of two special inequalities and applies algebraic transformation. This paper gives the triangular proof method of this kind of inequality. It is convenient for writing, agreed △ ABC three sides length, half perimeter, circumcircle radius, The inscribed circle radii are respectively a, b, c, s, R, r; where the proof of the example uses the following familiar triangle identities: abc=4Rrs, ∑bc=s2+4Rr+r2, and ∑a2=2 ( s2-4Rr-r2)