Question

如图:等腰三角形ABC中,顶角角A=36度,BD平分角ABC,则AD:AC=________.

Answer 1

等腰三角形ABC,顶角角A=36度,BD平分角ABC,

可知:AD=BD=BC ,所以AD/AC =BC/AC

根据余弦定理:cosA=(2AC^2-BC^2)/(2 x AC^2)

cos36`=1-BC^2/(2 x AC^2)

BC^2/AC^2=(1-cos36`) x 2

BC/AC =根号下(2-2cos36`)

即:AD/AC=根号下(2-2cos36`)