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∴∠PCB+∠ACD=90°,∴∠DAC=∠PCB. 又∵∠DAC=∠CAO,∴∠CAO=∠PCB.
∵CE平分∠ACB,∴∠ACF=∠BCF,∴∠CAO+∠ACF=∠PCB+∠BCF, ∴∠PFC=∠PCF,∴PC=PF,∴△PCF是等腰三角形. (3)连接AE.∵CE平分∠ACB,∴
=
,
∴AE=BE=72.
∵AB为⊙O的直径,∴∠AEB=90°.
在Rt△ABE中,AB?AE2?BE2?14. ∵∠PAC=∠PCB,∠P=∠P,∴△PAC∽△PCB,
PCAC?. PBBC4AC4PC4?,∴?. 又∵tan∠ABC=,∴
3BC3PB3∴
设PC=4k,PB=3k,
则在Rt△POC中,PO=3k+7,OC=7,
222
∵PC+OC=OP,
222
∴(4k)+7=(3k+7),∴k=6 (k=0不合题意,舍去). ∴PC=4k=4×6=24.
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26.解:(1)令y=0,则ax﹣6ax﹣16a=0,
2
∵a<0,∴x﹣6x﹣16=0,∴x1=﹣2,x2=8,∴A(﹣2,0),B(8,0), ∴OA=2,OB=8.
22
∵∠ACB=90°,OC⊥AB,∴△AOC∽△COB,∴OC=OA·OB,∴OC=2×8=16,
2
又OC>0,∴OC=4,∴C(0,4).把点C(0,4)代入y=ax﹣6ax﹣16a, 得﹣16a=4,解得a=?1123,∴y=?x+x+4;
244(2)①设直线BD的解析式为y=kx+b,
∵点C,D关于x轴对称,∴D(0,﹣4).把点B,点D的坐标代入上式,
1?k??8k?b?0?得?,解得?2, ?b??4??b??41∴直线BD的解析式为y=x﹣4.
21231设Q(m,?m+m+4),M(m,m﹣4),
224123112
∴QM=(?m+m+4)﹣(m﹣4)=?m+m+8.
224412
故答案为?m+m+8;
4②如图1,过点C作CN⊥QM于N. ∵S四边形CQBM=S△QMC+S△QMB=
11111QM·CN+QM·PB=QM(CN+PB)=QM(OP+PB)=QM·OB, 2222211222
∴S四边形CQBM=×(?m+m+8)×8=﹣m+4m+32=﹣(m﹣2)+36,
24∴当m等于2时,四边形CQBM的面积取得最大值,且最大值为36;
(3)当点P在线段EB上运动时,存在点Q(﹣2,0)或Q(6,4),使△BDQ为直角三角形.理由如下:
分三种情况:①当∠QBD=90°时,如图2.
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∵∠QBP+∠PBD=90°,∠PBD+∠BDO=90°,∴∠QBP=∠BDO, ∴tan∠QBP=tan∠BDO,即(?1232
m+m+4):(8﹣m)=8:4,整理,得m﹣14m+48=0,
24解得m1=6,m2=8(舍去),∴Q(6,4);
②当∠BDQ=90°时,显然点Q与点A重合,∴Q(﹣2,0);
③当∠BQD=90°时,以BD为直径的圆应该过点Q,但是,不难发现,以BD为直径的圆经过点O,与抛物线的交点是B,故不存在符合题意的点Q; 综上所述,所求点Q的坐标为(6,4)或(﹣2,0).
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英语试卷参考答案(二)
I.1-5 CABBA II.6-10 BBACB III.11-15 CACAC 16-18 CBC IV.19-21 CAB 22-25 ACAC V. 26-30 ADADD 31-35 CCACA 36-40 ADBDC 41-45 DCCCC VI. 46-50 ACDBA 51-55 CCCAA VII. 56-60 ABDAD 61-65 BDACC 66-70 DCBAB
VIII. 71. 110 islands 72. Seawater / Sea water 73. 117 (one hundred and seventeen) 74. from place to place 75. boat trips
IX. 76. an important change / a chance to be close to nature
77. Because they think being close to nature is good for children. / Because they think the survival activities are good for children. 78. terrible/ bad / dangerous
79. Many people think the survival activities are good for children. 80.甚至多年以后,他们仍将记得他们所学到的东西。
X. 81. Germans 82. twelfth 83. fewest 84. given up 85. lost XI. A) 86. I live in a two-floor family house. 87. Who did you go to the museum with? 88. Have you ever worked in a store? 89. He left without a word yesterday. 90. The clothing store is having a sale.
B) 91. We did a survey about whether we should help the old when they fall down, and here are the results. Only a small percentage of people think they will help the old, while 42% of people refuse to help the old ,also there are some people who say it’s not easy to say. In my opinion, we should help the old people , because we all have parents, and we will grow old one day. If all of us are not willing to give our hands, how can we ask others to help ourselves?
So I strongly call on people to show your love to the old, not only for others but also for ourselves.
附:听力录音材料
2015年河北省初中毕业生升学文化课考试(二)听力部分。听力部分共分两小节。第一节为选择题;第二节为非选择题。两部分分别在卷I和卷II。 现在是听力试音时间。
M: Excuse me, but could you tell me how to get to the cinema? W: Which cinema? M: The Capital Cinema.
W: Oh, it’s a long way from here. You’d better take a bus. M: Which bus shall I take then? W: I think you need to take No. 7.
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M: Thanks a lot. W: You’re welcome. 试音到此结束。
听力部分(第一节)
第一题:听句子,选出句子中所包含的信息。下面你将听到五个句子,每个句子读两遍。请你听完句子的第二遍朗读后,从各小题所给出的A、B、C三个选项中,选出包含所听信息的选项。
No. 1. I called you today, but your phone was out of service. No. 2. The accident happened on March 8th. No. 3. The police came and put out the fire.
No. 4. She studied hard so that she could pass the exam. No. 5. There was a large garden once upon a time.
第二题:听句子,选出该句的最佳答语。下面你将听到五个句子,每个句子读两遍。请你听完句子的第二遍朗读后,从各小题所给出的A、B、C三个选项中,选出该句的最佳答语。 No. 6. How often do you see a movie? No. 7. I think Teahouse is a play, not a place. No. 8. Can I have a brown skirt?
No. 9. You can’t drive too fast on the street, sir. No. 10. What about going skating this Sunday?
第三题:听对话和问题,选择正确的选项。下面你将听到五组对话和八个问题,每组对话和问题读两遍。请你听完对话和问题的第二遍朗读后,从各小题所给出的A、B、C三个选项中,选出正确选项。
请听第一至三组对话,并回答第11~13题。 No. 11.M: Which school team are you on?
W: I’m on the ping-pong team. What about you?
M: I’m on the badminton team, but I want to join the basketball team. Q: Which team is the boy on? No. 12.W: I have a toothache.
M: Maybe you should give up drinking so much cola. Q: What may the girl like drinking? No. 13.W: This story isn't scary, is it?
M: Actually, it is.
W: It is?! I'm really surprised! I was sure this story wasn't scary! Q: What does the man think of the story? 请听第四组对话,并回答第14至15题。 M: What a beautiful beach! And it is really a fine day! W: Yes. Hey, look at this beautiful stone!
M: it’s beautiful. Why don’t we pick some more and give our friends as gifts? W: Great!
Questions No. 14. How is the weather now?
Questions No. 15. What will the speakers give to their friends as gifts? 请听第五组对话,并回答第16至18题。 W: Mike, you look worried.
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