{"code":0,"msg":"success","data":[[{"head_title":"单选题","questions":[{"question_id":"4080587","question_type":"1","question_channel_type":"1","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"1","difficult_index":"5","master_level":"2","exam_type":"1","evaluated":"0","region_ids":"20","grade_id":"9","question_source":"2017年广西贵港市中考数学试卷 ","mode":"2","title":"(2017•贵港)如图,在Rt△ABC中,∠ACB=90°,将△ABC绕顶点C逆时针旋转得到△A'B'C,M是BC的中点,P是A'B'的中点,连接PM.若BC=2,∠BAC=30°,则线段PM的最大值是( )
","kid_num":"1","paperid":"211838","save_num":"299","oldqid":"0","explain_sort_need":"0","paper":{"pid":"211838","title":"2017年广西贵港市中考数学试卷 "},"extra_file":"","question_text":"如图,在Rt△ABC中,∠ACB=90°,将△ABC绕顶点C逆时针旋转得到△A'B'C,M是BC的中点,P是A'B'的中点,连接PM.若BC=2,∠BAC=30°,则线段PM的最大值是( )
","options":{"A":"4","B":"3","C":"2","D":"1"},"sub_explanation":null,"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":"2"},"sort":1,"sort2":1,"is_use":0},{"question_id":"4218307","question_type":"1","question_channel_type":"1","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"1","difficult_index":"3","master_level":"2","exam_type":"1","evaluated":"0","region_ids":"31","grade_id":"9","question_source":"2017年新疆乌鲁木齐市中考数学试卷","mode":"2","title":"(2017•乌鲁木齐)如图,点A(a,3),B(b,1)都在双曲线y= 3x 上,点C,D,分别是x轴,y轴上的动点,则四边形ABCD周长的最小值为( )","kid_num":"2","paperid":"221951","save_num":"230","oldqid":"0","explain_sort_need":"0","paper":{"pid":"221951","title":"2017年新疆乌鲁木齐市中考数学试卷"},"extra_file":"","question_text":"如图,点A(a,3),B(b,1)都在双曲线y= 上,点C,D,分别是x轴,y轴上的动点,则四边形ABCD周长的最小值为( )
","options":{"A":"","B":"","C":"","D":""},"sub_explanation":null,"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":"2"},"sort":2,"sort2":2,"is_use":0},{"question_id":"6487781","question_type":"1","question_channel_type":"1","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"1","difficult_index":"3","master_level":"4","exam_type":"2","evaluated":"0","region_ids":"1","grade_id":"8","question_source":"北京市东城区2015-2016学年八年级上学期数学期末考试试卷","mode":"2","title":"如图,正方形ABCD的面积为12,△ABE是等边三角形,点E在正方形ABCD内,在对角线AC上有一点P,使PD+PE最小,则这个最小值为( )","kid_num":"1","paperid":"663013","save_num":"80","oldqid":"0","explain_sort_need":"0","paper":{"pid":"663013","title":"北京市东城区2015-2016学年八年级上学期数学期末考试试卷"},"extra_file":"","question_text":"如图,正方形ABCD的面积为12,△ABE是等边三角形,点E在正方形ABCD内,在对角线AC上有一点P,使PD+PE最小,则这个最小值为( )","options":{"A":"","B":"2 ","C":"2 ","D":""},"sub_explanation":null,"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":"","score":{"score":"2"},"sort":3,"sort2":3,"is_use":0}],"scores":{"4080587":{"score":"2"},"4218307":{"score":"2"},"6487781":{"score":"2"}},"sum_score":6,"question_num":3},{"head_title":"填空题","questions":[{"question_id":"1586986","question_type":"4","question_channel_type":"4","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"2","exam_type":"1","evaluated":"0","region_ids":"","grade_id":"9","question_source":"广西崇左市江州区2020年数学中考一模试卷","mode":"2","title":"(2015•广州)如图,四边形ABCD中,∠A=90°,AB=3,AD=3,点M,N分别为线段BC,AB上的动点(含端点,但点M不与点B重合),点E,F分别为DM...","kid_num":"2","paperid":"2847172","save_num":"122","oldqid":"0","explain_sort_need":"0","paper":{"pid":"2847172","title":"广西崇左市江州区2020年数学中考一模试卷"},"extra_file":"","question_text":"如图,四边形ABCD中,∠A=90°,AB=3 , AD=3,点M,N分别为线段BC,AB上的动点(含端点,但点M不与点B重合),点E,F分别为DM,MN的中点,则EF长度的最大值为 .
","options":"","sub_explanation":[""],"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":{"1":""},"score":{"score":1,"subScore":1},"sort":4,"sort2":4,"is_use":0},{"question_id":"4064710","question_type":"4","question_channel_type":"4","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"2","exam_type":"1","evaluated":"0","region_ids":"24","grade_id":"9","question_source":"2017年贵州省安顺市中考数学试卷 ","mode":"2","title":"(2017•安顺)如图所示,正方形ABCD的边长为6,△ABE是等边三角形,点E在正方形ABCD内,在对角线AC上有一点P,使PD+PE的和最小,则这个最小值为.","kid_num":"3","paperid":"211065","save_num":"71","oldqid":"0","explain_sort_need":"0","paper":{"pid":"211065","title":"2017年贵州省安顺市中考数学试卷 "},"extra_file":"","question_text":"如图所示,正方形ABCD的边长为6,△ABE是等边三角形,点E在正方形ABCD内,在对角线AC上有一点P,使PD+PE的和最小,则这个最小值为.
","options":"","sub_explanation":[""],"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":{"1":""},"score":{"score":1,"subScore":1},"sort":5,"sort2":5,"is_use":0},{"question_id":"3650645","question_type":"4","question_channel_type":"4","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"2","exam_type":"1","evaluated":"0","region_ids":"11","grade_id":"9","question_source":"2015年浙江省台州市中考数学试卷","mode":"2","title":"(2015•台州)如图,正方形ABCD的边长为1,中心为点O,有一边长大小不定的正六边形EFGHIJ绕点O可任意旋转,在旋转过程中,这个正六边形始...","kid_num":"2","paperid":"160398","save_num":"68","oldqid":"0","explain_sort_need":"0","paper":{"pid":"160398","title":"2015年浙江省台州市中考数学试卷"},"extra_file":"","question_text":"如图,正方形ABCD的边长为1,中心为点O,有一边长大小不定的正六边形EFGHIJ绕点O可任意旋转,在旋转过程中,这个正六边形始终在正方形ABCD内(包括正方形的边),当这个正六边形的边长最大时,AE的最小值为.
","options":"","sub_explanation":[""],"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":{"1":""},"score":{"score":1,"subScore":1},"sort":6,"sort2":6,"is_use":0},{"question_id":"1556495","question_type":"4","question_channel_type":"4","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"2","exam_type":"1","evaluated":"0","region_ids":"","grade_id":"9","question_source":"","mode":"2","title":"(2015•陕西)如图,AB是⊙O的弦,AB=6,点C是⊙O上的一个动点,且∠ACB=45°.若点M,N分别是AB,BC的中点,则MN长的最大值是 ","kid_num":"3","paperid":"0","save_num":"80","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"如图,AB是⊙O的弦,AB=6,点C是⊙O上的一个动点,且∠ACB=45°.若点M,N分别是AB,BC的中点,则MN长的最大值是
","options":"","sub_explanation":[""],"knowledge":null,"category":null,"is_collect":false,"done":false,"myanswer":{"1":""},"score":{"score":1,"subScore":1},"sort":7,"sort2":7,"is_use":0}],"scores":{"1556495":{"score":1},"1586986":{"score":1},"3650645":{"score":1},"4064710":{"score":1}},"sum_score":4,"question_num":4},{"head_title":"综合题","questions":[{"question_id":"4059184","question_type":"7","question_channel_type":"28","is_explain":"1","is_on_sale":"1","question_status":"2","chid":"3","xd":"2","parent_id":"0","is_objective":"0","difficult_index":"3","master_level":"2","exam_type":"1","evaluated":"0","region_ids":"10","grade_id":"9","question_source":"2017年江苏省徐州市中考数学试卷 ","mode":"2","title":"(2017•徐州)如图,将边长为6的正三角形纸片ABC按如下顺序进行两次折叠,展平后,得折痕AD,BE(如图①),点O为其交点.","kid_num":"2","paperid":"210070","save_num":"74","oldqid":"0","explain_sort_need":"0","paper":{"pid":"210070","title":"2017年江苏省徐州市中考数学试卷 "},"extra_file":"","question_text":"如图,将边长为6的正三角形纸片ABC按如下顺序进行两次折叠,展平后,得折痕AD,BE(如图①),点O为其交点.
","options":"","sub_explanation":null,"list":[{"question_id":"34059642","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"zhongfangzhi","create_uid":"7263239","create_date":"2017-06-30 05:41:05","update_by":"","update_uid":"0","update_date":"2024-01-25 09:46:16","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"4059184","sort":8,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"探求AO到OD的数量关系,并说明理由;","options":"","answer":"解:AO=2OD,理由:∵△ABC是等边三角形,
∴∠BAO=∠ABO=∠OBD=30°,
∴AO=OB,
∵BD=CD,
∴AD⊥BC,
∴∠BDO=90°,
∴OB=2OD,
∴OA=2OD;
","answer_json":["解:AO=2OD,
理由:∵△ABC是等边三角形,
∴∠BAO=∠ABO=∠OBD=30°,
∴AO=OB,
∵BD=CD,
∴AD⊥BC,
∴∠BDO=90°,
∴OB=2OD,
∴OA=2OD;
"],"explanation":"","pic_answer":"0","pic_explanation":"0","sub_explanation":null,"knowledge":null,"category":null,"done":false,"myanswer":"","sort2":1},{"question_id":"34059650","qsn_id":null,"question_type":"5","question_channel_type":"0","is_explain":"0","is_on_sale":"0","question_status":"0","question_tags":"","chid":"3","xd":"2","create_by":"zhongfangzhi","create_uid":"7263239","create_date":"2017-06-30 05:41:05","update_by":"","update_uid":"0","update_date":"2024-01-25 09:46:16","update_reason":"","audit_by":"","audit_uid":"0","audit_date":null,"audit2_by":"","audit2_uid":"0","audit2_date":null,"opinion":null,"parent_id":"4059184","sort":9,"is_objective":"0","difficult_index":"0","master_level":"0","exam_type":"0","evaluated":"0","region_ids":"","grade_id":"0","question_source":"","mode":"2","is_delete":"0","md5sum":"","title":"","kid_num":"0","paperid":"0","save_num":"0","oldqid":"0","explain_sort_need":"0","paper":null,"extra_file":"","question_text":"如图②,若P,N分别为BE,BC上的动点.(Ⅰ)当PN+PD的长度取得最小值时,求BP的长度;
(Ⅱ)如图③,若点Q在线段BO上,BQ=1,则QN+NP+PD的最小值= .
","options":"","answer":"如图②,作点D关于BE的对称点D′,过D′作D′N⊥BC于N交BE于P,
则此时PN+PD的长度取得最小值,
∵BE垂直平分DD′,
∴BD=BD′,
∵∠ABC=60°,
∴△BDD′是等边三角形,
∴BN= BD= ,
∵∠PBN=30°,
∴ = ,
∴PB= ;
如图③,作Q关于BC的对称点Q′,作D关于BE的对称点D′,
连接Q′D′,即为QN+NP+PD的最小值.
根据轴对称的定义可知:∠Q′BN=∠QBN=30°,∠QBQ′=60°,
∴△BQQ′为等边三角形,△BDD′为等边三角形,
∴∠D′BQ′=90°,
∴在Rt△D′BQ′中,
D′Q′= = .
∴QN+NP+PD的最小值= ,
故答案为: .
","answer_json":["如图②,作点D关于BE的对称点D′,过D′作D′N⊥BC于N交BE于P,
则此时PN+PD的长度取得最小值,
∵BE垂直平分DD′,
∴BD=BD′,
∵∠ABC=60°,
∴△BDD′是等边三角形,
∴BN= BD= ,
∵∠PBN=30°,
∴ = ,
∴PB= ;
如图③,作Q关于BC的对称点Q′,作D关于BE的对称点D′,
连接Q′D′,即为QN+NP+PD的最小值.
根据轴对称的定义可知:∠Q′BN=∠QBN=30°,∠QBQ′=60°,
∴△BQQ′为等边三角形,△BDD′为等边三角形,
∴∠D′BQ′=90°,
∴在Rt△D′BQ′中,
D′Q′= = .
∴QN+NP+PD的最小值= ,
故答案为: .
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