本文给出如下一个条件几何不等式及其应用 .定理　在△ ABC中 ,a,b,c,R分别是∠ A,∠ B,∠C的对边长及外接圆半径 ,若1 50°≥∠C-∠B≥ 30°,则R2≥abcos C,( * )等号当且仅当∠ A=90°,∠ B=30°,∠ C=6 0°时成立 .证明　由正弦定理知 :a=2 Rsin A,b=2 Rsin B,abcos C- R2 = This paper gives a conditional geometric inequality and its application. Theorem In △ ABC, a, b, c, R are the length of the opposite side of ∠ A, ∠ B, ∠C and the radius of the circumscribed circle, if 1 50° ≥ ∠ C-∠B≥30°, then R2≥abcos C, the (*) equal sign is established if and only if ∠A=90°, ∠B=30°, ∠C=6 0°. Prove by the sine theorem: a=2 Rsin A, b=2 Rsin B,abcos C- R2 =