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解答题 | 一般(0.65) | 2021·全国高三专题练习
2 . 如图所示,有一块等腰三角形形状的空地eqIda670baf5d73f4d7689915a00c51820f2,腰eqId1eb64606273a4d63bfa90e56f9a3f5c2的长为3,底eqId99a3187c2b8f4bcc9703c74c3b72f1f3的长为4,现决定在该空地内筑一条笔直的小路eqId0f11c2065e3f45ff8c936750f661157c(宽度不计),将该空地分成一个四边形和一个三角形,设分成的四边形和三角形的周长相等,面积分别为eqIde0b0a69153d74086acac0f2b28878deceqIdc36de5c6d722440e9911d9802c4068f8.
说明: figure
(1)若小路一端EeqIdcf2da96900c948a1b3ce7cbfd420c080的中点,求此时小路的长度;
(2)求eqIdb297e74e95ff430b8bcf66c687849ca5的最小值.
4 . 在eqId7d9a9f629a9249f9b27148eed1fce4a5中,eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3所对的边长为eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqId44925af6fb19413689ba5616e3647cbaeqId7d9a9f629a9249f9b27148eed1fce4a5的面积为eqId51d8a094ee99497ea839941c67407d85,若eqId460073099ffa4d13817158bfdd03d864,则eqId87143b2d312446498115d9361f017f80的最大值为(   )
A.eqIde4d58f42bad9461b93d451da718fc6f4B.eqIdbf4d8b310ca74c22a7eb63a406f4674aC.eqId6a23198196a146a6b8ebcc8c83e0da5bD.eqIdd90d42b6b616485585b2c5a5bd194eb6
填空题 | 一般(0.65) | 2021·全国高一课时练习
5 . 在eqId64b9b599fdb6481e9f8d9a94c102300b中,abc为角ABC的对边,且eqId90edc9aab5b84946aca43933663c419f,则B的取值范围是___________.
6 . 在eqId64b9b599fdb6481e9f8d9a94c102300b中,角eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3所对的边分别为eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqId44925af6fb19413689ba5616e3647cba,已知eqId07b1fc08ee0f4a7f9677e727e2ab40aaeqId84d89de8bdfb4aaca7967c5e60408f42的平分线交eqIdcf2da96900c948a1b3ce7cbfd420c080于点eqId312ef2c826304089b9b0f1d1e88b0f50,且eqIdf3f694e24c46401a9ed71873211a45fb.有以下四个结论:
eqIdda3a13fdfc884e1fa88999218bd4f288
eqId6fd5fc4083ee4e79a9e4a9c42f57596e的最小值为eqIdc052ddfbd4524f67a79e0e77c2e5656a
eqId703f2317c5ab49bab8cdb65760991839的最小值为eqIdc052ddfbd4524f67a79e0e77c2e5656a
eqId57aafec16c0943f799f702411c9d3d16的最小值为eqId162460205087478e9e016cec007c9cf5
其中所有正确结论的编号为(   )
A.①③④B.②④C.①③D.①④
7 . 在△ABC中,角ABC的对边分别为abceqId91ee6799d0e3486ca8eea444889a16ce.
(1)求A
(2)若a=2,lS分别表示△ABC的周长和面积,求eqIdeb341eb9b5ed43de8bc1331d0c623281的最大值.
8 . 在eqId64b9b599fdb6481e9f8d9a94c102300b中,角eqId10bbe48f886a4fa78fdf8c1fd064f9b4的对边为eqId0ce93bfa1f6a4a23b3258410dd19847a,若eqIddd02993ec97e4035a08bd417ba2f42a5,则当eqId19a4eb16029e4550a14f2afe4741a3c3取最大值时,eqId64b9b599fdb6481e9f8d9a94c102300b的面积是(   )
A.eqIda0a63338a10c422289029e7524739222B.eqIda1b78c9af44346ddb4d164e485b4b8a7C.eqId94460cf1cc4e42958c160b907390e33dD.eqIda2a0ce3781fa4c26b624f5966b7dee44
9 . 从以下给出的①、②两个条件中任选一个,补充在下面的横线上,并加以解答.
eqId5a3b23e6b0e54916bfea871281e4f41e,②eqId0a527ec5534144aea4d88d4410c960bd已知eqId64b9b599fdb6481e9f8d9a94c102300b的内角eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3所对的边分别是eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqId44925af6fb19413689ba5616e3647cba,若______.
(1)求角eqId8754ce8cf7f34f04abb9a0c041f57f5c的值;
(2)求eqId64b9b599fdb6481e9f8d9a94c102300b的面积取得最大值eqIda2a0ce3781fa4c26b624f5966b7dee44时,边eqIdaea992e70d4943e49e893817eb885ed7的长.
10 . 设eqId64b9b599fdb6481e9f8d9a94c102300b的内角,内角eqId052844cae8574a8ab842c38a039baac0eqId8754ce8cf7f34f04abb9a0c041f57f5ceqId19a4eb16029e4550a14f2afe4741a3c3的对边分别为eqId70a27b6ddf6b478285353abb3b1f3741eqIdaea992e70d4943e49e893817eb885ed7eqId44925af6fb19413689ba5616e3647cbaeqId05bff4adb7ce4dbcae3264c845e51f5aeqId7626d02402f84ba1a6e4f6ff93710d39,则下列选项正确的是(   )
A.eqId64b9b599fdb6481e9f8d9a94c102300b外接圆半径为eqIdf7d6b53ad41c46fdaa1cbdb9c26ced4dB.eqId64b9b599fdb6481e9f8d9a94c102300b面积的最大值为eqId62f2412997424b4ca41272f35d432557
C.eqId64b9b599fdb6481e9f8d9a94c102300b的周长的最大值为8D.eqIdf82588160a0949bfb113971fad9a7f72的最大值为32