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已知三棱锥eqId12175c05cfe240a0b8270ee03df1962f的四个顶点都在球O的球面上,eqId829c3b65802b41feb4db730b8af793c5eqIdb60bb1649c8b41cb935771acc097167eeqIdd480b55f7fa24c9badf8a773686365bbeqId1a4ee4d443234c40969626092de88c44EF分别为eqIdcf2da96900c948a1b3ce7cbfd420c080eqIde9b50933e347462ea824ccc9bf51fc93的中点,eqId80b8ef2afe864b16aa2a9d494a6a0f6d,则球O的体积为______.
更新:2020/2/21难度:0.65题型:填空题组卷:0
正方体eqId588284d93dc5489295f8f224f8e30d13(棱长为1)中,点P在线段eqIdbf4db7d066034b139ff80a09ab139d45上(点P异于AD两点),线段eqIde4682078ddd9488281e376503edb4f95的中点为点Q,若平面eqId947905ffef4f44ed9736ed033482ddaa截该正方体所得的截面为四边形,则线段eqIdc390e4cf2bc742088263f6b3d1902201的取值范围为(   )
A.eqIdf5965b4286ad455f9954c3f3a09787faB.eqId46074e036c07436fb72e4593af0372b8C.eqId708882fbf3ff463dafb2169590a6e7f6D.eqIdb8c6753cb0a0447788c417ed8b177129
更新:2020/2/21难度:0.65题型:单选题组卷:0
已知两定点eqId25e81b8bd3424e438ace3b13a1b3b419eqIdb94d9eb225d84cbaad15b75dc72c0506,点P满足eqId4cf9bee08c9548f8a1b92d351839fd73.
(1)求点P的轨迹C的方程;
(2)若eqId027716c95f1f427fa078124e0f13aab2,直线l与轨迹C交于AB两点,eqId890174c35d994035b942963f9fddd43beqId6c7ff2dd96df49099993988f46d91119的斜率之和为2,问直线l是否恒过定点,若过定点,求出定点的坐标;若不过定点,请说明理由.
更新:2020/2/21难度:0.65题型:解答题组卷:0
三棱柱eqId9881c5faa5cb449bb37fa59b41c76e43中,棱eqId6736f952eef94c70a9c5dbaa0da8831eeqId99a3187c2b8f4bcc9703c74c3b72f1f3eqId17ceafc9b1a74a37a89907801af1e742的中点分别是PQO.
figure
(1)求证:eqId0942fdb579de40088689da76fdfee53c平面eqId6bdc14d2f1ca4a4f8d1fcef031c45ccc
(2)若三棱柱eqId9881c5faa5cb449bb37fa59b41c76e43的体积为eqId6cd972e243e54a85b083a2e95b353bc9,求三棱柱eqIdd32955d568c742bd8c0747eb2672a046的体积.
更新:2020/2/21难度:0.65题型:解答题组卷:0
如图,平面eqId20605163b3294217a96bac7d1b539498平面eqId89fbdcb029be4482b52165366491c70f,四边形eqId63d825051bb849e2af689f782774767a为矩形,且eqId97c02d46b11c4b1cb9e38d70c787b584,eqId63db14a5b4334f3ea583c8fb12b0d175eqId92869ac114124367b45f631d030ed6bd分别为eqIdbf4db7d066034b139ff80a09ab139d45eqId5bc8e1134afb4130a2c2d1a5b3e30dd6的中点.
figure
(1)求证:eqId4cf12eb3bb3a4719b08e1d3ec6600296平面eqId89fbdcb029be4482b52165366491c70f;
(2)求证:平面eqIdf0cfde295583466b9dbac068cefc5734平面eqIda3c6f0e7f58b4f259c1664244e2084e8.
更新:2020/2/21难度:0.65题型:解答题组卷:0
在正方体eqId588284d93dc5489295f8f224f8e30d13中,给出下列结论:①eqIdd22d18ebf1104e83919799759cb4ae99;②eqId1b3546c62d874298b57d3ddefabe97ec;③eqId1ed5c9a541554ff2bbacbddf4d0638c6eqId3be2cc74b5df4257b116d1672859cb5e所成的角为eqId1a06b2701ed24e619837f7dc479f5e9d;④eqId99a3187c2b8f4bcc9703c74c3b72f1f3eqId710b690db05c4a9ca514d234b961f314所成的角为eqIdb7fe117dc1a94fbf93716ecbbcced6bd.其中所有正确结论的序号为______.
更新:2020/2/21难度:0.85题型:填空题组卷:0
已知圆eqId19a4eb16029e4550a14f2afe4741a3c3的圆心在直线eqId6219c25b80844355984283f98d485885.
(1)若圆eqId19a4eb16029e4550a14f2afe4741a3c3eqId072d7d6b911b42bc89207e72515ebf5f轴的正半轴相切,且该圆截eqId8e15963708e9415da25069fea5906e24轴所得弦的长为eqId7bcd573cee334383ad72cc4b179fcfb3,求圆eqId19a4eb16029e4550a14f2afe4741a3c3的标准方程;
(2)在(1)的条件下,直线eqId2ddef28a78634518af3f536f7c5e0c3e与圆eqId19a4eb16029e4550a14f2afe4741a3c3交于两点eqIdcc614bd3390c4d028df189b234dcc351,eqId8754ce8cf7f34f04abb9a0c041f57f5c,若以eqId99a3187c2b8f4bcc9703c74c3b72f1f3为直径的圆过坐标原点eqId2efda802d5534f6d92d9f8af7aaec28b,求实数eqIdaea992e70d4943e49e893817eb885ed7的值;
(3)已知点eqId6fe7026f09c9416e906fe61e2457c0bb,圆eqId19a4eb16029e4550a14f2afe4741a3c3的半径为3,且圆心eqId19a4eb16029e4550a14f2afe4741a3c3在第一象限,若圆eqId19a4eb16029e4550a14f2afe4741a3c3上存在点eqId2381423d4cd146cab95f55527681a766,使eqId759c1f00840a4ba89e4ff4b0e3571bbf(eqId2efda802d5534f6d92d9f8af7aaec28b为坐标原点),求圆心eqId19a4eb16029e4550a14f2afe4741a3c3的纵坐标的取值范围.
更新:2020/2/21难度:0.65题型:解答题组卷:0
如图,eqIde34726e130e14183a5fc4272dc576bfc是圆柱的轴截面,eqId19a4eb16029e4550a14f2afe4741a3c3是底面圆周上异于eqIdcc614bd3390c4d028df189b234dcc351,eqId8754ce8cf7f34f04abb9a0c041f57f5c的一点,eqId1c81f185076946de9e53b6a97f9123a2.
figure
(1)求证:平面eqId14d628d0dbda4df4bb8e2d0f38d982b8平面eqIdb3ae382132044585a5c3f1aeb81c2c74;
(2)若eqIdb139c1fed7c44076817a8330c676ffa8,求几何体eqId0539cb32d6014cc4819c9138d0a0804d的体积eqId25ff966f0d37438092ad538565a6569d.
更新:2020/2/21难度:0.65题型:解答题组卷:0
如图,在正方体eqId588284d93dc5489295f8f224f8e30d13中,点EeqId99a3187c2b8f4bcc9703c74c3b72f1f3中点.
figure
(1)证明:eqIdf7dc88da7f064e57870260332912743f平面eqId694c3b99d07441b89d2f58bd7dc97685
(2)求直线eqId3639203bd3084ad4a35ca2e4a0eb4ea2与平面eqIdcda0c05de34247558016c1afea57aa4e所成角的正弦值.
更新:2020/2/21难度:0.65题型:解答题组卷:0
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