收录高三寒假作业34新题
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20240125-115018
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023883:023888
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20240125-115315
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023889:023896
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@ -299526,7 +299526,9 @@
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"20221111\t周双"
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"remark": "",
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"space": "4em",
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@ -368312,7 +368314,9 @@
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"20230118\t王伟叶"
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],
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"same": [],
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"related": [
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"remark": "",
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@ -485989,7 +485993,9 @@
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"20230606\t王伟叶"
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],
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"same": [],
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"related": [],
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"related": [
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"023896"
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"remark": "",
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"space": "4em",
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@ -644368,6 +644374,174 @@
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"space": "4em",
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"unrelated": []
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},
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"023889": {
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"id": "023889",
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"content": "平行六面体 $ABCD-A_1B_1C_1D_1$ 中, $M$ 为 $AC$ 与 $BD$ 的交点, 设 $\\overrightarrow{A_1B_1}=\\overrightarrow{a}$, $\\overrightarrow{A_1D_1}=\\overrightarrow{b}$,\n$\\overrightarrow{AA_1}=\\overrightarrow{c}$, 则 $\\overrightarrow{B_1M}=$\\blank{50}. (用 $\\overrightarrow{a}$、$\\overrightarrow{b}$、$\\overrightarrow{c}$ 表示)",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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],
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"same": [],
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"related": [
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"010715"
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],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023890": {
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"id": "023890",
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"content": "下列所有命题中正确的命题序号是\\blank{50}.\\\\\n\\textcircled{1} 若 $|\\overrightarrow{a}|=|\\overrightarrow{b}|$, 则 $\\overrightarrow{a}, \\overrightarrow{b}$ 的长度相同, 方向相反或相同; \\textcircled{2} 若 $\\overrightarrow{a}$ 与 $\\overrightarrow{b}$ 是互为负向量, 则 $|\\overrightarrow{a}|=|\\overrightarrow{b}|$; \\textcircled{3} 空间向量的加法满足结合律; \\textcircled{4} 在四边形 $ABCD$ 中, 一定有 $\\overrightarrow{AB}+\\overrightarrow{AD}=\\overrightarrow{AC}$.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023891": {
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"id": "023891",
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"content": "在正四面体 $O-ABC$ 中, $\\overrightarrow{OA}=\\overrightarrow{a}$, $\\overrightarrow{OB}=\\overrightarrow{b}$, $\\overrightarrow{OC}=\\overrightarrow{c}, D$ 为 $BC$ 的中点, $E$ 为 $AD$ 的中点, 则 $\\overrightarrow{OE}=$\\blank{50}. (用 $\\overrightarrow{a}$、$\\overrightarrow{b}$、$\\overrightarrow{c}$ 表示)",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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],
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"same": [],
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"related": [
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"013151"
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],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023892": {
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"id": "023892",
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"content": "给出下列命题: \\textcircled{1} 空间任意两个向量 $\\overrightarrow{a}$、$\\overrightarrow{b}$ 一定是共面的; \\textcircled{2} $\\overrightarrow{a}$、$\\overrightarrow{b}$ 为空间两个向量, 则 $|\\overrightarrow{a}|=|\\overrightarrow{b}| \\Leftrightarrow \\overrightarrow{a}=\\overrightarrow{b}$; \\textcircled{3} 若 $\\overrightarrow{a}\\parallel \\overrightarrow{b}$, 则 $\\overrightarrow{a}$ 与 $\\overrightarrow{b}$ 所在直线平行; \\textcircled{4} 如果 $\\overrightarrow{a}\\parallel \\overrightarrow{b}$、$\\overrightarrow{b}\\parallel \\overrightarrow{c}$, 那么 $\\overrightarrow{a}\\parallel \\overrightarrow{c}$. 其中假命题的序号是\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023893": {
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"id": "023893",
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"content": "已知向量 $\\overrightarrow{AB}$、$\\overrightarrow{AC}$、$\\overrightarrow{BC}$ 满足 $|\\overrightarrow{AB}|=|\\overrightarrow{AC}|+|\\overrightarrow{BC}|$, 则有\\bracket{20}.\n\\fourch{$\\overrightarrow{AB}=\\overrightarrow{AC}+\\overrightarrow{BC}$}{$\\overrightarrow{AB}=-\\overrightarrow{AC}-\\overrightarrow{BC}$}{$\\overrightarrow{AC}$ 与 $\\overrightarrow{BC}$ 同向}{$\\overrightarrow{AC}$ 与 $\\overrightarrow{CB}$ 同向}",
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"objs": [],
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"tags": [],
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"genre": "选择题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023894": {
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"id": "023894",
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"content": "已知向量 $\\overrightarrow{a}=\\overrightarrow{x}+2 \\overrightarrow{y}-\\overrightarrow{z}$, 且 $|\\overrightarrow{x}|=|\\overrightarrow{y}|=|\\overrightarrow{z}|=1$, 若向量 $\\overrightarrow{x}$、$\\overrightarrow{y}$、$\\overrightarrow{z}$ 两两垂直, 则 $|\\overrightarrow{a}|=$\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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],
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"same": [],
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"related": [],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023895": {
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"id": "023895",
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"content": "已知平行六面体 $ABCD-A' B' C' D'$ 中, $AB=4$, $AD=3$, $AA'=5$, $\\angle BAD=90^{\\circ}$, $\\angle BAA'=\\angle DAA'=60^{\\circ}$, 则$|AC'|=$\\blank{50}.",
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"objs": [],
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"tags": [],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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],
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"same": [],
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"related": [
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"040598"
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],
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"remark": "",
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"space": "",
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"unrelated": []
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},
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"023896": {
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"id": "023896",
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"content": "如图, 已知 $M$、$N$ 分别为四面体 $A-BCD$ 的面 $BCD$ 与面 $ACD$ 的重心, $G$ 为 $AM$ 上一点, 且 $GM: GA=1: 3$. 求证: $B$、$G$、$N$ 三点共线.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0,0) node [left] {$B$} coordinate (B);\n\\draw (2,0,0) node [right] {$D$} coordinate (D);\n\\draw (1,0,{sqrt(3)}) node [below] {$C$} coordinate (C);\n\\draw ($1/3*(D)+1/3*(B)+1/3*(C)$) ++ (0,{2*sqrt(6)/3},0) node [above] {$A$} coordinate (A);\n\\draw (A)--(B)(A)--(C)(A)--(D)(B)--(C)--(D);\n\\draw [dashed] (B)--(D);\n\\draw (A)--(B)--(C)--(D)--cycle(A)--(C);\n\\draw [dashed] (B)--(D);\n\\filldraw ($1/3*(D)+1/3*(B)+1/3*(C)$) node [below] {$M$} coordinate (M) circle (0.03);\n\\filldraw ($1/3*(D)+1/3*(A)+1/3*(C)$) node [below] {$N$} coordinate (N) circle (0.03);\n\\filldraw ($(A)!0.75!(M)$) node [left] {$G$} coordinate (G) circle (0.03);\n\\draw [dashed] (A)--(M);\n\\end{tikzpicture}\n\\end{center}",
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"objs": [],
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"tags": [],
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"genre": "解答题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "自拟题目",
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"edit": [
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"20240125\t毛培菁"
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],
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"same": [],
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"related": [
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"017992"
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"space": "4em",
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},
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"030001": {
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"id": "030001",
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"content": "若$x,y,z$都是实数, 则:(填写``\\textcircled{1} 充分非必要、\\textcircled{2} 必要非充分、\\textcircled{3} 充要、\\textcircled{4} 既非充分又非必要''之一)\\\\\n(1) ``$xy=0$''是``$x=0$''的\\blank{50}条件;\\\\\n(2) ``$x\\cdot y=y\\cdot z$''是``$x=z$''的\\blank{50}条件;\\\\\n(3) ``$\\dfrac xy=\\dfrac yz$''是``$xz=y^2$''的\\blank{50}条件;\\\\\n(4) ``$|x |>| y|$''是``$x>y>0$''的\\blank{50}条件;\\\\\n(5) ``$x^2>4$''是``$x>2$'' 的\\blank{50}条件;\\\\\n(6) ``$x=-3$''是``$x^2+x-6=0$'' 的\\blank{50}条件;\\\\\n(7) ``$|x+y|<2$''是``$|x|<1$且$|y|<1$'' 的\\blank{50}条件;\\\\\n(8) ``$|x|<3$''是``$x^2<9$'' 的\\blank{50}条件;\\\\\n(9) ``$x^2+y^2>0$''是``$x\\ne 0$'' 的\\blank{50}条件;\\\\\n(10) ``$\\dfrac{x^2+x+1}{3x+2}<0$''是``$3x+2<0$'' 的\\blank{50}条件;\\\\\n(11) ``$0<x<3$''是``$|x-1|<2$'' 的\\blank{50}条件.",
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"20230410\t王伟叶"
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],
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"same": [],
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"related": [],
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"related": [
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"023895"
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],
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"remark": "",
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"space": "4em",
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"unrelated": []
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