Question

1.在等腰三角形ABC中,顶角角A为36度,BD为角ABC的平分线,求AD/AC的值.(好象要用到黄金分割点)

Answer 1

∵ AB=AC∴∠ ABC=∠C又∵∠ A=36 ∴∠ABC=∠C=72

∵BD平分∠B ∴∠ ABD=∠DBC=36 ∠C=∠BDC=72

∴AD=BD =CD

∵∠A=∠DBC ∠ C=∠C∴△ABC∽△BCD∴AB/BD=BC/DC ∵ AB=AC,DC=AC-AD BC=AD

∴ AC/AD=AD/(AC-DC) ∴ AC/AD =(1±√5)/2舍负 ∴ AC/AD =(1+√5)/2

∴ AD/AC =2/(1+√5)=（√5-1)/2

2 ∵EF‖BC∴△ AEF∽△ADB又∵ AE/ED=2 ∴EF/DB=2/（2+1）=2/3

在直角△ACD中