运河数学网（ http://yhsxw.vicp.net ） 2010中考真题 ∴C（1，23）. ···························· 3分 ⑵①在Rt△ACE中，tan∠CAE=
CE?3， AE∴∠CAE=60o，
由抛物线的对称性可知l是线段AB的垂直平分线， ∴AC=BC，
∴△ABC为等边三角形， ···················································· 4分 ∴AB= BC =AC = 4，∠ABC=∠ACB= 60o， 又∵AM=AP，BN=BP， ∴BN = CM，
∴△ABN≌△BCM， ∴AN=BM. ········································································ 5分 ②四边形AMNB的面积有最小值． ········································ 6分 设AP=m，四边形AMNB的面积为S，
3由①可知AB= BC= 4，BN = CM=BP，S△ABC=×42=43，
4∴CM=BN= BP=4－m，CN=m， 过M作MF⊥BC,垂足为F,
3(4?m)， 则MF=MC?sin60o=233211(4?m)=?m?3m， ∴S△CMN=CN?MF=m?···················· 7分 2422∴S=S△ABC－S△CMN
32m?3m） =43－（?4=3(m?2)2?33 ····························································· 8分 4∴m=2时，S取得最小值33. ·············································· 9分
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