河南省禹州市2014-2015学年八年级数学四科联赛决赛试题(扫描版)

河南省禹州市2014-2015学年八年级数学四科联赛决赛试题(扫描版)
河南省禹州市2014-2015学年八年级数学四科联赛决赛试题(扫描版)

河南省禹州市2014-2015学年八年级数学四科联赛决赛试题

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三、解答题:(本大题共5个小题,满分44分)

17、(6分)解: 分三种情况:

(1)AB=AC ,∠BAC=90°,AD ⊥BC ,∴BD=DC.又AD =2

1BC ,∴AD=BD ,CD=AD.∴∠BAD=∠ABD=45°,∠CAD=∠C=45°,∴∠BAC=∠BAD+∠CAD=45°+45°=90°.

(2)AB=BC ,0<∠ABC <90°,AD ⊥BC ,∵AD=

21BC ,∴AD=21AB ,∴∠ABC=30°,∴∠BAC=75°.

(3)AB=BC ,90°<∠ABC <180°,AD ⊥BC ,∵AD=21BC ,∴AD=2

1AB ,∴∠ABD=30°,∴∠BAC=15°.综上,∠BAC 的度数为90°或75°或15°.

19、(8分)解:由12=++c b a ,568222=+-+c c b a ,

有c b a 21-=+,568222+-=+c c b a .

∵ab b a b a 2)(222-+=+,∴ab c c c 2)21(56822--=+-,∴222-+-=c c ab .∴

原式=2)21()22()(2-=---+-=+-c c c c b a c ab .

20、(10分)解:(1)2003605430=??÷

;(2)如图; (3)?=?36360200

20; (4)1200200

60901600=+?(个).

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