本文提出并证明以下关于三角形的两个不等式。 1°△ABC的内切圆分别切各边于A’,B’,C’,则 △A’B’C’的面积≤1/△ABC的面积 (1)式中等号当且只当△ABC为等边三角形时成立: 2°设△ABC的外接圆半径为R,内切圆半径为ρ,顶点A,B,C到内心的距离分别为α,β,γ,则有 32Rρ~5≤α~2β~2γ~2 (2) This paper proposes and proves the following two inequalities about triangles. The inscribed circle of 1°ΔABC cuts each side to A′, B′, and C′, then the area of ​​△A′B′C′ is less than or equal to the area of ​​△ABC (1) if the number is equal to, and only if △ When ABC is an equilateral triangle, it is established: 2° Let △ABC have a circumcircle radius of R, an inscribed circle radius of ρ, and the distances of vertices A, B, and C to the heart are α, β, and γ, and 32Rρ~5. ≤α~2β~2γ~2 (2)