Question

如图,在三角形ABC中,∠C=90°,BC=a,CA =b,AB=c

Answer 1

选择A.

由内心性质知

OE/OA=a/b+c,OF/OB=b/a+c .

又因为c2=a2+b2,

所以,S△OEF/S△OAB=OE・OF/OA・OB = ab/ (b+c)(a+c)=2ab/2(ab+ac+bc+c2)=2ab/a2+b2+c2 +2ab+2bc+2ca= (a+b+c)(a+b-c)/(a+b+c) 2 =a+b-c/ a+b+c