Question

如图,点M （2,2）将一个90度的角尺的直角顶点放在M处角尺……用初二的方法做

Answer 1

SΔOAB=1/2OA.OB=1/2(AB+OA+OB)ON

OA+OB=4(这个应该很好证明)

OA.OB=(AB+4)ON

(OA+OB)2=OA2+OB2+2OA.OB

因为OA2+OB2＝AB2

16= AB2+2OA.OB= AB2+2(AB+4)ON

AB2+2(AB+4)ON-16=0

(AB+4) (AB-4) +2(AB+4)ON=0

(AB+4) (AB-4 +2ON)=0

AB-4 +2ON=0或AB+4＝0

1/2AB+ON=2