三角形ABC内接于圆O,AB=AC,P为弧BC上一点如图1,角BAC=60,延长PC到D,使cd=pb,连接ad,(pb+pc)/ap=?如图2,角BAC=90,则(PB+PC)/PA=?,如图3,角BAC=2α,则(PB+PC)/PA=?(用含α的三角函数的式子表示)
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![三角形ABC内接于圆O,AB=AC,P为弧BC上一点如图1,角BAC=60,延长PC到D,使cd=pb,连接ad,(pb+pc)/ap=?如图2,角BAC=90,则(PB+PC)/PA=?,如图3,角BAC=2α,则(PB+PC)/PA=?(用含α的三角函数的式子表示)](/uploads/image/z/10174681-1-1.jpg?t=%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E5%86%85%E6%8E%A5%E4%BA%8E%E5%9C%86O%2CAB%3DAC%2CP%E4%B8%BA%E5%BC%A7BC%E4%B8%8A%E4%B8%80%E7%82%B9%E5%A6%82%E5%9B%BE1%2C%E8%A7%92BAC%3D60%2C%E5%BB%B6%E9%95%BFPC%E5%88%B0D%2C%E4%BD%BFcd%3Dpb%2C%E8%BF%9E%E6%8E%A5ad%2C%28pb%2Bpc%29%2Fap%3D%3F%E5%A6%82%E5%9B%BE2%2C%E8%A7%92BAC%3D90%2C%E5%88%99%28PB%2BPC%29%2FPA%3D%3F%2C%E5%A6%82%E5%9B%BE3%2C%E8%A7%92BAC%3D2%CE%B1%2C%E5%88%99%28PB%2BPC%29%2FPA%3D%3F%28%E7%94%A8%E5%90%AB%CE%B1%E7%9A%84%E4%B8%89%E8%A7%92%E5%87%BD%E6%95%B0%E7%9A%84%E5%BC%8F%E5%AD%90%E8%A1%A8%E7%A4%BA%29)
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三角形ABC内接于圆O,AB=AC,P为弧BC上一点如图1,角BAC=60,延长PC到D,使cd=pb,连接ad,(pb+pc)/ap=?如图2,角BAC=90,则(PB+PC)/PA=?,如图3,角BAC=2α,则(PB+PC)/PA=?(用含α的三角函数的式子表示)
三角形ABC内接于圆O,AB=AC,P为弧BC上一点
如图1,角BAC=60,延长PC到D,使cd=pb,连接ad,(pb+pc)/ap=?
如图2,角BAC=90,则(PB+PC)/PA=?,
如图3,角BAC=2α,则(PB+PC)/PA=?(用含α的三角函数的式子表示)
三角形ABC内接于圆O,AB=AC,P为弧BC上一点如图1,角BAC=60,延长PC到D,使cd=pb,连接ad,(pb+pc)/ap=?如图2,角BAC=90,则(PB+PC)/PA=?,如图3,角BAC=2α,则(PB+PC)/PA=?(用含α的三角函数的式子表示)
(1)∵A、B、P、C四点共圆
∴∠ACD=∠ABP
∵AB=AC BP=CD
∴⊿ABP≌⊿ACD
∴AP=AD ∠D=∠APB=∠ACB
∵∠B=∠APD
∴⊿APD∽⊿ABC
∴(PC+CD)/AD=BC/AC即(PC+CB)/PA=BC/AC
∴∠BAC=60° AB=AC
∴AB=BC=AC
∴(PC+PB)/PA=1
(2)同上,(PB+PC)/pA=BC/AC.
∵∠BAC=90° AB=AC
∴BC=√2AC
∴(PB+PC)/PA=√2
(3)同(1)(PB+PC)/PA=BC/AC
∵∠BAC=α AB=AC
∴BC=2AC*sin(α/2)
∴(PB+PC)/PA=2sin(α/2)