26.如图.六边形ABCDEF内接于半径为r的⊙O.其中AD为直径.且AB=CD=DE=FA. (1)当∠BAD=75°时.求的长, (2)求证:BC∥AD∥FE, (3)设AB=.求六边形AB——青夏教育精英家教网—

26.如图.六边形ABCDEF内接于半径为r的⊙O.其中AD为直径.且AB=CD=DE=FA. (1)当∠BAD=75°时.求的长, (2)求证:BC∥AD∥FE, (3)设AB=.求六边形ABCDEF的周长L关于的函数关系式.并指出为何值时.L取得最大值. 26．(1)连结OB.OC.由∠BAD=75°.OA=OB知∠AOB=30°. ∵AB=CD.∴∠COD=∠AOB=30°.∴∠BOC=120°.···················· 故的长为．····················································································· (2)连结BD.∵AB=CD.∴∠ADB=∠CBD.∴BC∥AD.················· 同理EF∥AD.从而BC∥AD∥FE．······················································ (3)过点B作BM⊥AD于M.由(2)知四边形ABCD为等腰梯形. 从而BC=AD-2AM=2r-2AM．·································································· ∵AD为直径.∴∠ABD=90°.易得△BAM∽△DAB ∴AM==.∴BC=2r-.同理EF=2r-·································· ∴L=4x+2(2r-)==.其中0＜x＜ · ∴当x=r时.L取得最大值6r．····························································· 13七. 【查看更多】

题目列表(包括答案和解析)

（2008•长沙）如图，六边形ABCDEF内接于半径为r（常数）的⊙O，其中AD为直径，且AB=CD=DE=FA．
（1）当∠BAD=75°时，求