Question

如图在三角形ABC中。AB=8 AC=4 G为BC的中点，DG垂直BC 交∠BAC的平分线AD 于D，DE垂直AB于E DF垂直AC

延长线于F 1 求证BE=CF 2 求AE的长

Answer 1

连接CD,BC
1, AD为∠BAC平分线DE⊥AB DF⊥AC
DE=DF
G为BC的中点,DG⊥BD
DC=DB
RT△DEB≌RT△DFC
BE=CF
2,AD为∠BAC平分线DE⊥AB DF⊥AC,AF=AE
CF=AF-AC BE=AB-AE
AF-AC=AB-AE AF=AE
AB-AC=2AE
AE=(8-4)/2=2

Answer 2

连接CD,BC
1, AD为∠BAC平分线DE⊥AB DF⊥AC
DE=DF
G为BC的中点,DG⊥BD
DC=DB
RT△DEB≌RT△DFC
BE=CF
2,AD为∠BAC平分线DE⊥AB DF⊥AC,AF=AE
CF=AF-AC BE=AB-AE
AF-AC=AB-AE AF=AE
AB-AC=2AE
AE=(8-4)/2=2