摘要：⌒ 线段的计算问题 [例1]如图.⊙O是以AB为直径的△ABC的外接圆.D是劣弧BC的中点.连AD并用处与过C点的切线交于P.OD与BC相交于E.求证:,(3)当AC = 6.AB = 10时.求切线PC的长, [例2]如图.BC为半圆的直径.O为圆心.BC = 10.AD与半圆相切于D.DA⊥AB.AD = 4.求tg∠AED的值,(3)求证:CD = DE, [例3]已知:如图.⊙O1与⊙O2相交于点A.B且点O1在⊙O2上.直线O1O2交⊙O1于点C.D.交⊙O2与点E.过点C作CF⊥CE.交EA的延长线与点F.若DE = 2.AE = 2.(1)求证:EF是⊙O1的切线,求tan∠DAE的值, [例4]如图.△ABC内接于⊙O.AB是⊙O的直径.PA是过A点的直线.∠PAC =∠B.(1)求证:PA是⊙O的切线,(2)如果弦CD交AB于E.CD的延长线交PA于F.AC = 8.CE∶ED = 6∶5.AE∶EB = 2∶3.求AB的长和∠ECB的正切值, [例5]如图.⊙O1和⊙O2内切于A.⊙O2的弦BC切⊙O1于D.AD的延长线交⊙O2于M.连AB.AC分别交⊙O1于E.F.连EF.求证:AB·AC = AD·AM,(3)若⊙O1的半径R1 = 3.⊙O2的半径R2 = 8.BC是⊙O2的直径.求AB和AC的长, [例6]如图.⊙O1和⊙O2外切于点P.A是⊙O1上一点.AC切⊙O2于点C.交⊙O1于点B. AP的延长线交⊙O2于点D.CP的延长线交⊙O1于点E.连AE.PB.CD.求证:,(3)当⊙O2的半径为.APPD = 97.tan∠CAD = 时.求切线AC的长, [热点考题训练]1.如图.⊙O分别切AB.AC于E.F.且交BC于M.N两点.∠A = 90°.∠B =∠C.EB = 1.△ABC的面积为S1.⊙O的面积为S2.S1∶S2 = 25∶32π.求BM. ⌒ ⌒

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