{"id":1672,"date":"2020-12-12T16:17:04","date_gmt":"2020-12-12T13:17:04","guid":{"rendered":"http:\/\/helloege.ru\/?page_id=1672"},"modified":"2021-12-09T15:11:40","modified_gmt":"2021-12-09T12:11:40","slug":"zadanie-5024","status":"publish","type":"page","link":"http:\/\/helloege.ru\/?page_id=1672","title":{"rendered":"\u0417\u0430\u0434\u0430\u043d\u0438\u0435 5024"},"content":{"rendered":"<p style=\"font-weight: 400;\">\u0412 \u043f\u0438\u0440\u0430\u043c\u0438\u0434\u0435\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;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;5&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 \">\\( 5\\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;2&lt;\/mn&gt;&lt;mo&gt;:&lt;\/mo&gt;&lt;mn&gt;3&lt;\/mn&gt;&lt;\/mrow&gt;&lt;\/semantics&gt;&lt;\/mstyle&gt;&lt;\/math&gt;\">DM:MA=DN:NC=2:3<\/span>. \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0441\u0435\u0447\u0435\u043d\u0438\u044f\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\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1679 size-full\" src=\"http:\/\/helloege.ru\/wp-content\/uploads\/2020\/12\/h5024_1.png\" alt=\"\u0412 \u043f\u0438\u0440\u0430\u043c\u0438\u0434\u0435\u00a0ABCD\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\\( 5\\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=2:3. \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0441\u0435\u0447\u0435\u043d\u0438\u044f\u00a0MNB.\" width=\"309\" height=\"384\" data-wp-pid=\"1679\" srcset=\"http:\/\/helloege.ru\/wp-content\/uploads\/2020\/12\/h5024_1.png 309w, http:\/\/helloege.ru\/wp-content\/uploads\/2020\/12\/h5024_1-241x300.png 241w\" sizes=\"(max-width: 309px) 100vw, 309px\" \/><\/p>\n<p style=\"font-weight: 400;\"><\/div><\/div> <div class=\"su-column su-column-size-1-2\"><div class=\"su-column-inner su-u-clearfix su-u-trim\"><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1675 size-full\" src=\"http:\/\/helloege.ru\/wp-content\/uploads\/2020\/12\/h5024_2.png\" alt=\"\u0412 \u043f\u0438\u0440\u0430\u043c\u0438\u0434\u0435\u00a0ABCD\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\\( 5\\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=2:3. \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0441\u0435\u0447\u0435\u043d\u0438\u044f\u00a0MNB.\" width=\"224\" height=\"338\" data-wp-pid=\"1675\" srcset=\"http:\/\/helloege.ru\/wp-content\/uploads\/2020\/12\/h5024_2.png 224w, http:\/\/helloege.ru\/wp-content\/uploads\/2020\/12\/h5024_2-199x300.png 199w\" sizes=\"(max-width: 224px) 100vw, 224px\" \/><\/p>\n<p style=\"font-weight: 400;\"><\/div><\/div><\/div>\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}|=5\\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 MB, MN, \u043f\u043b\u043e\u0449\u0430\u0434\u044c <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><\/p>\n<hr \/>\n<p>\u041e\u0442\u0432\u0435\u0442; \u200b<span class=\"math inherit-color \">\\( \\sqrt{54} \\)<\/span>\u200b<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0412 \u043f\u0438\u0440\u0430\u043c\u0438\u0434\u0435\u00a0ABCD\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\\( 5\\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=2:3. \u041d\u0430\u0439\u0434\u0438\u0442\u0435 \u043f\u043b\u043e\u0449\u0430\u0434\u044c \u0441\u0435\u0447\u0435\u043d\u0438\u044f\u00a0MNB. \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\\( |\\vec{AB}|=|\\vec{BC}|=|\\vec{CA}|=5\\sqrt{2} \\)\u200b\u00a0 \u00a0\u0414\u043e\u043a\u0430\u0437\u0430\u0442\u044c, \u0447\u0442\u043e\u00a0 \u00a0x=y=z. \u041d\u0430\u0439\u0442\u0438 x. \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 &hellip; <\/p>\n<p class=\"link-more\"><a href=\"http:\/\/helloege.ru\/?page_id=1672\" class=\"more-link\">\u0427\u0438\u0442\u0430\u0442\u044c \u0434\u0430\u043b\u0435\u0435<span class=\"screen-reader-text\"> \u00ab\u0417\u0430\u0434\u0430\u043d\u0438\u0435 5024\u00bb<\/span><\/a><\/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\/1672"}],"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=1672"}],"version-history":[{"count":12,"href":"http:\/\/helloege.ru\/index.php?rest_route=\/wp\/v2\/pages\/1672\/revisions"}],"predecessor-version":[{"id":1690,"href":"http:\/\/helloege.ru\/index.php?rest_route=\/wp\/v2\/pages\/1672\/revisions\/1690"}],"wp:attachment":[{"href":"http:\/\/helloege.ru\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1672"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}