![\"\"](\"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/9.png?resize=1024%2C576&ssl=1\")
<\/figure>\n\n\n\n- \n
- O \u2014 \u015brodek ko\u0142a<\/li>\n\n\n\n
- OA \u2014 promie\u0144 ko\u0142a<\/li>\n<\/ul>\n\n\n\n
Co to jest okr\u0105g?<\/h2>\n\n\n\n
Okr\u0105g to ko\u0142o wraz ze swoim wewn\u0119trznym obszarem. Zapami\u0119taj: ko\u0142o to linia, okr\u0105g to p\u0142aszczyzna. Na rysunku pokazano r\u00f3\u017cnic\u0119 mi\u0119dzy ko\u0142em a okr\u0119giem w codziennym \u017cyciu.<\/p>\n\n\n\n
![\"\"](\"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/10.png?resize=1920%2C1080&ssl=1\")
<\/figure>\n\n\n\n- \n
- Talerz to okr\u0105g, ma powierzchni\u0119.<\/li>\n\n\n\n
- Bransoletka to ko\u0142o, ma tylko lini\u0119.<\/li>\n<\/ul>\n\n\n\n
Co to s\u0105 ci\u0119ciwa i \u015brednica?<\/h2>\n\n\n\n
- \n
- Ci\u0119ciwa \u0142\u0105czy dwa punkty na okr\u0119gu.<\/li>\n\n\n\n
- Je\u015bli ci\u0119ciwa przechodzi przez \u015brodek ko\u0142a, nazywa si\u0119 \u015brednic\u0105.<\/li>\n\n\n\n
- \u015arednica r\u00f3wna si\u0119 dw\u00f3m promieniom.<\/li>\n<\/ul>\n\n\n\n
![\"\"](\"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/11.png?resize=1920%2C1080&ssl=1\")
<\/figure>\n\n\n\n- \n
- AB \u2014 \u015brednica ko\u0142a<\/li>\n\n\n\n
- CD \u2014 ci\u0119ciwa ko\u0142a<\/li>\n<\/ul>\n\n\n\n
Co to jest r\u00f3wnanie okr\u0119gu?<\/h2>\n\n\n\n
R\u00f3wnanie okr\u0119gu ze \u015brodkiem w punkcie O i promieniem r wygl\u0105da tak:<\/p>\n\n\n\\[\\left(x-x_0\\right)^2+\\left(y-y_0\\right)^2=r^2\\]\n\n\n\n
Gdzie \ud835\udc31\u2080, \ud835\udc32\u2080 – wsp\u00f3\u0142rz\u0119dne \u015brodka ko\u0142a. Wszystkie warto\u015bci x i y, kt\u00f3re spe\u0142niaj\u0105 to r\u00f3wnanie, znajduj\u0105 si\u0119 na okr\u0119gu. Na podstawie tego r\u00f3wnania mo\u017cna utworzy\u0107 wz\u00f3r do znajdowania promienia okr\u0119gu.<\/p>\n\n\n\\[r=\\sqrt{\\left(x-x_0\\right)^2+\\left(y-y_0\\right)^2}\\]\n\n\n\n
Jak znale\u017a\u0107 d\u0142ugo\u015b\u0107 okr\u0119gu?<\/h2>\n\n\n\n
D\u0142ugo\u015b\u0107 okr\u0119gu mo\u017cna znale\u017a\u0107 znaj\u0105c promie\u0144 lub \u015brednic\u0119 okr\u0119gu. D\u0142ugo\u015b\u0107 okr\u0119gu oznacza si\u0119 liter\u0105 L.<\/p>\n\n\n\\[l=2\\pi r,;l;=\\pi d\\]\n\n\n\n
Co to jest styczna do okr\u0119gu?<\/h2>\n\n\n\n
Je\u015bli prosta i okr\u0105g maj\u0105 jeden wsp\u00f3lny punkt, tak\u0105 prost\u0105 nazywaj\u0105 styczn\u0105. Je\u015bli poprowadzi\u0107 promie\u0144 do tego punktu, zawsze b\u0119dzie on prostopad\u0142y do stycznej.<\/p>\n\n\n\n
![\"\"](\"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2023\/11\/dotichna.png?resize=1024%2C576&ssl=1\")
<\/figure>\n\n\n\n- \n
- OA \u2014 promie\u0144 okr\u0119gu, prostopad\u0142y do stycznej<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"
W tym artykule platforma edukacyjna Mathema wyja\u015bnia najwa\u017cniejsze poj\u0119cia zwi\u0105zane z tematem \u201eKo\u0142o i okr\u0105g\u201d w szkolnej geometrii. Dowiesz si\u0119, […]<\/p>\n","protected":false},"author":15,"featured_media":61233,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_glsr_average":0,"_glsr_ranking":0,"_glsr_reviews":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[37,3384],"tags":[],"class_list":["post-130564","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-blog","category-szkola-srednia"],"acf":[],"jetpack_featured_media_url":"https:\/\/i0.wp.com\/mathema.me\/wp-content\/uploads\/2024\/02\/post-cover-77.jpg?fit=1080%2C675&ssl=1","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/posts\/130564","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=130564"}],"version-history":[{"count":1,"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/posts\/130564\/revisions"}],"predecessor-version":[{"id":178187,"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/posts\/130564\/revisions\/178187"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/media\/61233"}],"wp:attachment":[{"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/media?parent=130564"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/categories?post=130564"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathema.me\/pl\/wp-json\/wp\/v2\/tags?post=130564"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- OA \u2014 promie\u0144 okr\u0119gu, prostopad\u0142y do stycznej<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"