{"id":1691,"date":"2020-12-13T20:21:49","date_gmt":"2020-12-13T17:21:49","guid":{"rendered":"http:\/\/helloege.ru\/?page_id=1691"},"modified":"2021-12-09T15:11:53","modified_gmt":"2021-12-09T12:11:53","slug":"zadanie-5043","status":"publish","type":"page","link":"http:\/\/helloege.ru\/?page_id=1691","title":{"rendered":"\u0417\u0430\u0434\u0430\u043d\u0438\u0435 5043"},"content":{"rendered":"<p style=\"font-weight: 400;\">\u0412 \u043f\u0438\u0440\u0430\u043c\u0438\u0434\u0435 <span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mstyle displaystyle=&quot;true&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;\/mi&gt;&lt;mi&gt;B&lt;\/mi&gt;&lt;mi&gt;C&lt;\/mi&gt;&lt;mi&gt;D&lt;\/mi&gt;&lt;\/mrow&gt;&lt;\/semantics&gt;&lt;\/mstyle&gt;&lt;\/math&gt;\">ABCD<\/span>\u00a0\u0440\u0451\u0431\u0440\u0430\u00a0<span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mstyle displaystyle=&quot;true&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;\/mi&gt;&lt;mi&gt;A&lt;\/mi&gt;&lt;\/mrow&gt;&lt;\/semantics&gt;&lt;\/mstyle&gt;&lt;\/math&gt;\">DA<\/span>,\u00a0<span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mstyle displaystyle=&quot;true&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;\/mi&gt;&lt;mi&gt;B&lt;\/mi&gt;&lt;\/mrow&gt;&lt;\/semantics&gt;&lt;\/mstyle&gt;&lt;\/math&gt;\">DB<\/span>\u00a0\u0438\u00a0<span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mstyle displaystyle=&quot;true&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;\/mi&gt;&lt;mi&gt;C&lt;\/mi&gt;&lt;\/mrow&gt;&lt;\/semantics&gt;&lt;\/mstyle&gt;&lt;\/math&gt;\">DC<\/span>\u00a0\u043f\u043e\u043f\u0430\u0440\u043d\u043e \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b, \u0430\u00a0<span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mstyle displaystyle=&quot;true&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;A&lt;\/mi&gt;&lt;mi&gt;B&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mi&gt;B&lt;\/mi&gt;&lt;mi&gt;C&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mi&gt;A&lt;\/mi&gt;&lt;mi&gt;C&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mn&gt;6&lt;\/mn&gt;&lt;msqrt&gt;&lt;mn&gt;2&lt;\/mn&gt;&lt;\/msqrt&gt;&lt;\/mrow&gt;&lt;\/semantics&gt;&lt;\/mstyle&gt;&lt;\/math&gt;\">AB=BC=AC=\u200b<span class=\"math inherit-color\">\\( 6\\sqrt{2} \\)<\/span>\u200b<\/span>.<\/p>\n<p style=\"font-weight: 400;\">\u0430)\u00a0\u0414\u043e\u043a\u0430\u0436\u0438\u0442\u0435, \u0447\u0442\u043e \u044d\u0442\u0430 \u043f\u0438\u0440\u0430\u043c\u0438\u0434\u0430 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u0430\u044f.<\/p>\n<p style=\"font-weight: 400;\">\u0431)\u00a0\u041d\u0430 \u0440\u0451\u0431\u0440\u0430\u0445\u00a0<span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mstyle displaystyle=&quot;true&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;\/mi&gt;&lt;mi&gt;A&lt;\/mi&gt;&lt;\/mrow&gt;&lt;\/semantics&gt;&lt;\/mstyle&gt;&lt;\/math&gt;\">DA<\/span>\u00a0\u0438\u00a0<span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mstyle displaystyle=&quot;true&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;\/mi&gt;&lt;mi&gt;C&lt;\/mi&gt;&lt;\/mrow&gt;&lt;\/semantics&gt;&lt;\/mstyle&gt;&lt;\/math&gt;\">DC<\/span>\u00a0\u043e\u0442\u043c\u0435\u0447\u0435\u043d\u044b \u0442\u043e\u0447\u043a\u0438\u00a0<span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mstyle displaystyle=&quot;true&quot;&gt;&lt;semantics&gt;&lt;mi&gt;M&lt;\/mi&gt;&lt;\/semantics&gt;&lt;\/mstyle&gt;&lt;\/math&gt;\">M<\/span>\u00a0\u0438\u00a0<span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mstyle displaystyle=&quot;true&quot;&gt;&lt;semantics&gt;&lt;mi&gt;N&lt;\/mi&gt;&lt;\/semantics&gt;&lt;\/mstyle&gt;&lt;\/math&gt;\">N<\/span>\u00a0\u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u043f\u0440\u0438\u0447\u0451\u043c\u00a0<span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mstyle displaystyle=&quot;true&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;D&lt;\/mi&gt;&lt;mi&gt;M&lt;\/mi&gt;&lt;mo&gt;:&lt;\/mo&gt;&lt;mi&gt;M&lt;\/mi&gt;&lt;mi&gt;A&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mi&gt;D&lt;\/mi&gt;&lt;mi&gt;N&lt;\/mi&gt;&lt;mo&gt;:&lt;\/mo&gt;&lt;mi&gt;N&lt;\/mi&gt;&lt;mi&gt;C&lt;\/mi&gt;&lt;mo&gt;=&lt;\/mo&gt;&lt;mn&gt;1&lt;\/mn&gt;&lt;mo&gt;:&lt;\/mo&gt;&lt;mn&gt;2&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/semantics&gt;&lt;\/mstyle&gt;&lt;\/math&gt;\">DM:MA=DN:NC=1:2<\/span>. \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0442\u043e\u0447\u043a\u0438\u00a0<span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mstyle displaystyle=&quot;true&quot;&gt;&lt;semantics&gt;&lt;mi&gt;D&lt;\/mi&gt;&lt;\/semantics&gt;&lt;\/mstyle&gt;&lt;\/math&gt;\">D<\/span>\u00a0\u0434\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438\u00a0<span data-mathml=\"&lt;math xmlns=&quot;http:\/\/www.w3.org\/1998\/Math\/MathML&quot;&gt;&lt;mstyle displaystyle=&quot;true&quot;&gt;&lt;semantics&gt;&lt;mrow&gt;&lt;mi&gt;M&lt;\/mi&gt;&lt;mi&gt;N&lt;\/mi&gt;&lt;mi&gt;B&lt;\/mi&gt;&lt;\/mrow&gt;&lt;\/semantics&gt;&lt;\/mstyle&gt;&lt;\/math&gt;\">MNB<\/span>.<div class=\"su-row\"><div class=\"su-column su-column-size-1-2\"><div class=\"su-column-inner su-u-clearfix su-u-trim\">\n<hr \/>\n<p>\u041e\u043f\u0440\u0435\u0434\u0435\u043b\u0438\u043c \u043a\u043e\u043e\u0440\u0434\u0438\u043d\u0430\u0442\u044b \u0442\u043e\u0447\u0435\u043a &#8212; C(x,0,0), B(0,y,0), A(0,0,z).\u00a0 \u0418\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0440\u0430\u0432\u0435\u043d\u0441\u0442\u0432\u043e \u200b<span class=\"math inherit-color\">\\( |\\vec{AB}|=|\\vec{BC}|=|\\vec{CA}|=6\\sqrt{2} \\)<\/span>\u200b\u00a0 \u00a0\u0414\u043e\u043a\u0430\u0437\u0430\u0442\u044c, \u0447\u0442\u043e\u00a0 \u00a0x=y=z. \u041d\u0430\u0439\u0442\u0438 x.<\/p>\n<p>\u0414\u043e\u043a\u0430\u0437\u0430\u0442\u044c, \u0447\u0442\u043e, \u0435\u0441\u043b\u0438 \u043e\u0434\u043d\u0430 \u0433\u0440\u0430\u043d\u044c \u0442\u0435\u0442\u0440\u0430\u044d\u0434\u0440\u0430 &#8212; \u043e\u0441\u043d\u043e\u0432\u0430\u043d\u0438\u0435 &#8212; \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u044b\u0439 \u0442\u0440\u0435\u0443\u0433\u043e\u043b\u044c\u043d\u0438\u043a, \u0430 \u0431\u043e\u043a\u043e\u0432\u044b\u0435 \u0440\u0435\u0431\u0440\u0430 \u0440\u0430\u0432\u043d\u044b \u043c\u0435\u0436\u0434\u0443 \u0441\u043e\u0431\u043e\u0439, \u0442\u043e \u0442\u0430\u043a\u043e\u0439 \u0442\u0435\u0442\u0440\u0430\u044d\u0434\u0440 &#8212; \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u0430\u044f \u043f\u0438\u0440\u0430\u043c\u0438\u0434\u0430.<\/p>\n<p>\u041d\u0430\u0439\u0442\u0438 DM, DN, DB. \u0421\u043e\u0441\u0442\u0430\u0432\u0438\u0442\u044c \u0443\u0440\u0430\u0432\u043d\u0435\u043d\u0438\u0435 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 MNB \u0438\u0441\u043f\u043e\u043b\u044c\u0437\u0443\u044f \u0444\u043e\u0440\u043c\u0443\u043b\u0443 \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u0432 \u043e\u0442\u0440\u0435\u0437\u043a\u0430\u0445.<\/p>\n<p>\u041d\u0430\u0439\u0442\u0438 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0442\u043e\u0447\u043a\u0438 D(0,0,0) \u0434\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438 \u200b<span class=\"math inherit-color \">\\( \\frac{x}{2}+\\frac{y}{6}+\\frac{z}{2}=1 \\)<\/span>\u200b.<\/p>\n<hr \/>\n<p>\u041e\u0442\u0432\u0435\u0442: \u200b<span class=\"math inherit-color \">\\( \\frac{6}{\\sqrt{19}} \\)<\/span>\u200b<\/p>\n<\/div><\/div> <div class=\"su-column su-column-size-1-2\"><div class=\"su-column-inner su-u-clearfix su-u-trim\">\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1693 size-full\" src=\"http:\/\/helloege.ru\/wp-content\/uploads\/2020\/12\/h5043_1.png\" alt=\"\u0412 \u043f\u0438\u0440\u0430\u043c\u0438\u0434\u0435 ABCD\u00a0\u0440\u0451\u0431\u0440\u0430\u00a0DA,\u00a0DB\u00a0\u0438\u00a0DC\u00a0\u043f\u043e\u043f\u0430\u0440\u043d\u043e \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b, \u0430\u00a0AB=BC=AC=\u200b\\( 6\\sqrt{2} \\)\u200b. \u0430)\u00a0\u0414\u043e\u043a\u0430\u0436\u0438\u0442\u0435, \u0447\u0442\u043e \u044d\u0442\u0430 \u043f\u0438\u0440\u0430\u043c\u0438\u0434\u0430 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u0430\u044f. \u0431)\u00a0\u041d\u0430 \u0440\u0451\u0431\u0440\u0430\u0445\u00a0DA\u00a0\u0438\u00a0DC\u00a0\u043e\u0442\u043c\u0435\u0447\u0435\u043d\u044b \u0442\u043e\u0447\u043a\u0438\u00a0M\u00a0\u0438\u00a0N\u00a0\u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u043f\u0440\u0438\u0447\u0451\u043c\u00a0DM:MA=DN:NC=1:2. \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0442\u043e\u0447\u043a\u0438\u00a0D\u00a0\u0434\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438\u00a0MNB.\" width=\"306\" height=\"388\" data-wp-pid=\"1693\" srcset=\"http:\/\/helloege.ru\/wp-content\/uploads\/2020\/12\/h5043_1.png 306w, http:\/\/helloege.ru\/wp-content\/uploads\/2020\/12\/h5043_1-237x300.png 237w\" sizes=\"(max-width: 306px) 100vw, 306px\" \/><\/div><\/div><\/div>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0412 \u043f\u0438\u0440\u0430\u043c\u0438\u0434\u0435 ABCD\u00a0\u0440\u0451\u0431\u0440\u0430\u00a0DA,\u00a0DB\u00a0\u0438\u00a0DC\u00a0\u043f\u043e\u043f\u0430\u0440\u043d\u043e \u043f\u0435\u0440\u043f\u0435\u043d\u0434\u0438\u043a\u0443\u043b\u044f\u0440\u043d\u044b, \u0430\u00a0AB=BC=AC=\u200b\\( 6\\sqrt{2} \\)\u200b. \u0430)\u00a0\u0414\u043e\u043a\u0430\u0436\u0438\u0442\u0435, \u0447\u0442\u043e \u044d\u0442\u0430 \u043f\u0438\u0440\u0430\u043c\u0438\u0434\u0430 \u043f\u0440\u0430\u0432\u0438\u043b\u044c\u043d\u0430\u044f. \u0431)\u00a0\u041d\u0430 \u0440\u0451\u0431\u0440\u0430\u0445\u00a0DA\u00a0\u0438\u00a0DC\u00a0\u043e\u0442\u043c\u0435\u0447\u0435\u043d\u044b \u0442\u043e\u0447\u043a\u0438\u00a0M\u00a0\u0438\u00a0N\u00a0\u0441\u043e\u043e\u0442\u0432\u0435\u0442\u0441\u0442\u0432\u0435\u043d\u043d\u043e, \u043f\u0440\u0438\u0447\u0451\u043c\u00a0DM:MA=DN:NC=1:2. \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u0440\u0430\u0441\u0441\u0442\u043e\u044f\u043d\u0438\u0435 \u043e\u0442 \u0442\u043e\u0447\u043a\u0438\u00a0D\u00a0\u0434\u043e \u043f\u043b\u043e\u0441\u043a\u043e\u0441\u0442\u0438\u00a0MNB. &nbsp;<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"aioseo_notices":[],"_links":{"self":[{"href":"http:\/\/helloege.ru\/index.php?rest_route=\/wp\/v2\/pages\/1691"}],"collection":[{"href":"http:\/\/helloege.ru\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"http:\/\/helloege.ru\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"http:\/\/helloege.ru\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/helloege.ru\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1691"}],"version-history":[{"count":8,"href":"http:\/\/helloege.ru\/index.php?rest_route=\/wp\/v2\/pages\/1691\/revisions"}],"predecessor-version":[{"id":1700,"href":"http:\/\/helloege.ru\/index.php?rest_route=\/wp\/v2\/pages\/1691\/revisions\/1700"}],"wp:attachment":[{"href":"http:\/\/helloege.ru\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1691"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}