{"id":145777,"date":"2024-07-26T13:38:02","date_gmt":"2024-07-26T10:38:02","guid":{"rendered":"https:\/\/mathema.me\/?p=145777"},"modified":"2024-09-25T18:45:33","modified_gmt":"2024-09-25T15:45:33","slug":"kolo-wpisane-w-trojkat","status":"publish","type":"post","link":"https:\/\/mathema.me\/pl\/blog\/kolo-wpisane-w-trojkat\/","title":{"rendered":"Ko\u0142o wpisane w tr\u00f3jk\u0105t. Podstawowe formu\u0142y i w\u0142a\u015bciwo\u015bci"},"content":{"rendered":"\n<p>Temat &#8222;Ko\u0142o wpisane w tr\u00f3jk\u0105t&#8221; jest omawiany w 8 klasie na lekcjach geometrii. Mathema przygotowa\u0142a artyku\u0142 o kole wpisanym w tr\u00f3jk\u0105t, jego w\u0142a\u015bciwo\u015bciach oraz formu\u0142ach do obliczania promienia takiego ko\u0142a.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Co to jest ko\u0142o wpisane w tr\u00f3jk\u0105t?<\/h3>\n\n\n\n<p>Ko\u0142o jest nazywane wpisanym w tr\u00f3jk\u0105t, gdy wszystkie boki tr\u00f3jk\u0105ta s\u0105 styczne do tego ko\u0142a. Dwusieczne k\u0105t\u00f3w tr\u00f3jk\u0105ta zawsze przecinaj\u0105 si\u0119 w jednym punkcie, kt\u00f3ry jest \u015brodkiem wpisanego ko\u0142a. Oznacza to, \u017ce w ka\u017cdy tr\u00f3jk\u0105t mo\u017cna wpisa\u0107 ko\u0142o.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img data-recalc-dims=\"1\" loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/kolo.png?resize=1024%2C576&#038;ssl=1\" alt=\"\" class=\"wp-image-121651\" srcset=\"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/kolo.png?resize=1024%2C576&amp;ssl=1 1024w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/kolo.png?resize=600%2C338&amp;ssl=1 600w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/kolo.png?resize=300%2C169&amp;ssl=1 300w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/kolo.png?resize=768%2C432&amp;ssl=1 768w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/kolo.png?resize=50%2C28&amp;ssl=1 50w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/kolo.png?resize=1600%2C900&amp;ssl=1 1600w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/kolo.png?resize=1536%2C864&amp;ssl=1 1536w, https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/kolo.png?w=1920&amp;ssl=1 1920w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>ABC \u2014 tr\u00f3jk\u0105t<\/li>\n\n\n\n<li>O \u2014 \u015brodek wpisanego ko\u0142a<\/li>\n\n\n\n<li>Czerwonym kolorem oznaczone s\u0105 dwusieczne<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Promie\u0144 ko\u0142a wpisanego w tr\u00f3jk\u0105t<\/h3>\n\n\n\n<p>Istnieje kilka sposob\u00f3w na znalezienie promienia ko\u0142a wpisanego w tr\u00f3jk\u0105t. R\u00f3\u017cni\u0105 si\u0119 one w zale\u017cno\u015bci od rodzaju tr\u00f3jk\u0105ta. Formu\u0142a do obliczania promienia ko\u0142a wpisanego w tr\u00f3jk\u0105t r\u00f3wnoboczny wygl\u0105da tak:<\/p>\n\n\n\n\\[r=\\frac13h,\\;r\\;=\\;\\frac{a\\sqrt3}6\\]\n\n\n\n<ul class=\"wp-block-list\">\n<li>h \u2014 wysoko\u015b\u0107 tr\u00f3jk\u0105ta<\/li>\n\n\n\n<li>a \u2014 bok tr\u00f3jk\u0105ta<\/li>\n<\/ul>\n\n\n\n<p>Formu\u0142a do obliczania promienia ko\u0142a wpisanego w dowolny tr\u00f3jk\u0105t:<\/p>\n\n\n\n\\[r=\\frac{S_\\triangle}p\\]\n\n\n\n<ul class=\"wp-block-list\">\n<li>p \u2014 p\u00f3\u0142obw\u00f3d<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Jak skonstruowa\u0107 ko\u0142o wpisane w tr\u00f3jk\u0105t<\/h2>\n\n\n\n<p>Aby skonstruowa\u0107 ko\u0142o wpisane w tr\u00f3jk\u0105t, nale\u017cy poprowadzi\u0107 dwusieczne k\u0105t\u00f3w tr\u00f3jk\u0105ta. Punkt przeci\u0119cia dwusiecznych b\u0119dzie \u015brodkiem ko\u0142a.<\/p>\n\n\n\n<p>Korepetytorzy online z matematyki dla 8 klasy, pracuj\u0105cy w Mathema, pomog\u0105 zrozumie\u0107 temat &#8222;Ko\u0142o wpisane w tr\u00f3jk\u0105t&#8221; w zaledwie kilka lekcji.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Temat &#8222;Ko\u0142o wpisane w tr\u00f3jk\u0105t&#8221; jest omawiany w 8 klasie na lekcjach geometrii. Mathema przygotowa\u0142a artyku\u0142 o kole wpisanym w [&hellip;]<\/p>\n","protected":false},"author":15,"featured_media":61353,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[37,3386],"tags":[],"class_list":["post-145777","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-blog","category-geometria"],"acf":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2024\/02\/post-cover-85.jpg?fit=1080%2C675&ssl=1","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/posts\/145777","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/users\/15"}],"replies":[{"embeddable":true,"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/comments?post=145777"}],"version-history":[{"count":1,"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/posts\/145777\/revisions"}],"predecessor-version":[{"id":178152,"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/posts\/145777\/revisions\/178152"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/media\/61353"}],"wp:attachment":[{"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/media?parent=145777"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/categories?post=145777"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/tags?post=145777"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}