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本文提出并证明了三角形中关于动点的几个不等式,尤其文中定理1所给出的不等式相当美妙有用,而且证法初等. 为以下行文方便,文中将统一采用以下记号:在△ABC中,BC=a,CA=b,AB=c,面积为△,外接圆半径为R,内切圆半径为r.P为△ABC内部或边界上任意一点,从P作△ABC的边BC、CA、AB所在的直线的垂线,垂足分别为D、E、F;记PA=R1,PB=R2,PC=R3,PD=r1,PE=r2,PF=r3(如图所示).另
This paper proposes and proves several inequalities about the moving points in the triangle, especially the inequality given in the theorem 1 in the paper is quite wonderful and useful, and the proof method is elementary. For the convenience of the following text, the following marks are uniformly used in the paper: In △ABC, BC=a, CA=b, AB=c, area is △, radius of circumcircle is R, radius of inscribed circle is rP is inside or on boundary of △ABC, edge of △ABC from P is BC, CA, AB The vertical line of the line, the foot is D, E, F respectively; remember PA = R1, PB = R2, PC = R3, PD = r1, PE = r2, PF = r3 (as shown).