{"paper":{"id":"site-2658","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","variant":null,"exam_pdf":null,"key_pdf":null,"question_count":9,"source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},"questions":[{"id":"site-2658/zad/3147","paper_id":"site-2658","number":"3147","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Zaznaczony na rysunku kąt alfa jest równy A. 50 stopni, B. 40 stopni, C. 30 stopni, D. 10 stopni.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2658/zad-3147.svg","solution_image":"img/site/2658/rozw-3147.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2658/zad/3148","paper_id":"site-2658","number":"3148","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Kąt między cięciwą AB a styczną do okręgu w punkcie A (zobacz rysunek) ma miarę 62 stopni. Wówczas A. beta = 118 stopni, B. beta = 124 stopni, C. beta = 138 stopni, D. beta = 152 stopni.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2658/zad-3148.svg","solution_image":"img/site/2658/rozw-3148.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2658/zad/3149","paper_id":"site-2658","number":"3149","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Kąt środkowy i kąt wpisany są oparte na tym samym łuku. Suma ich miar jest równa 180. Jaka jest miara kąta środkowego? A. 60 stopni, B. 90 stopni, C. 120 stopni, D. 135 stopni","answer":null,"answer_text":null,"solution":null,"image":"img/site/2658/zad-3149.svg","solution_image":"img/site/2658/rozw-3149.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2658/zad/4353","paper_id":"site-2658","number":"4353","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Na okręgu o środku S leżą punkty A, B, C i D. Odcinek AB jest średnicą tego okręgu. Kąt między tą średnicą a cięciwą AC jest równy 21 stopni (zobacz rysunek). A. 21 stopni, B. 42 stopni, C. 48 stopni, D. 69 stopni.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2658/zad-4353.svg","solution_image":"img/site/2658/rozw-4353.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2658/zad/5317","paper_id":"site-2658","number":"5317","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Punkty A, B, C, D leżą na okręgu o środku w punkcie O. Kąt środkowy DOC ma miarę 118° (zobacz rysunek). Miara kąta ABC jest równa A. 59°; B. 48°; C. 62°; D. 31°.","answer":null,"answer_text":null,"solution":null,"image":"img/site/2658/zad-5317.svg","solution_image":"img/site/2658/rozw-5317.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2658/zad/5476","paper_id":"site-2658","number":"5476","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Rozwiązanie zadania. Trójkąt ABC jest wpisany w okrąg o środku O. Miara kąta CAO jest równa 70° (zobacz rysunek). Wtedy miara kąta ABC jest równa A. 20° B. 25° C. 30° D. 35°","answer":null,"answer_text":null,"solution":null,"image":"img/site/2658/zad-5476.svg","solution_image":"img/site/2658/rozw-5476.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2658/zad/6667","paper_id":"site-2658","number":"6667","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Odcinek AB jest średnicą okręgu o środku w punkcie O i promieniu r=8 (zobacz rysunek). Cięciwa AC ma długość 8√3. [rysunek] Miara kąta BAC jest równa A. 30° B. 45° C. 15° D. 60°","answer":null,"answer_text":null,"solution":null,"image":"img/site/2658/zad-6667.svg","solution_image":"img/site/2658/rozw-6667.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2658/zad/6670","paper_id":"site-2658","number":"6670","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Punkty A oraz B leżą na okręgu o środku O. Proste k i l są styczne do tego okręgu w punktach - odpowiednio - A i B. Te proste przecinają się w punkcie S i tworzą kąt o mierze 76° (zobacz rysunek). [rysunek] Miara kąta OBA jest równa A. 52° B. 26° C. 14° D. 38°","answer":null,"answer_text":null,"solution":null,"image":"img/site/2658/zad-6670.svg","solution_image":"img/site/2658/rozw-6670.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"},{"id":"site-2658/zad/8156","paper_id":"site-2658","number":"8156","points":null,"ptype":"open","subject":"matematyka","category":"zbiory","year":0,"month":null,"level":"podstawowa","text":"Cztery różne punkty: A, B, C oraz D, leżą na okręgu o środku w punkcie S. Odcinek AC jest średnicą tego okręgu. Cięciwa BD przecina tę średnicę. Oznaczmy przez β miarę kąta wpisanego DBC, natomiast przez γ - miarę kąta wpisanego ACD (zobacz rysunek). [rysunek] Suma β + γ jest równa A. 60° B. 90° C. 120° D. 135°","answer":null,"answer_text":null,"solution":null,"image":"img/site/2658/zad-8156.svg","solution_image":"img/site/2658/rozw-8156.svg","topics":null,"page_from":null,"source":"site","answer_source":null,"answer_text_source":null,"solution_source":null,"text_source":"site","source_label":"Matematyka · Zbiory zadań (podstawowa)","subject_label":"Matematyka","category_label":"Zbiory zadań"}]}