Definicja 1
Kołem o środku w punkcie O i promieniu r, r>0,
nazywamy zbiór wszystkich punktów płaszczyzny których odległość od punktu O
jest mniejsza od r lub równa r. Takie koło oznaczamy symbolem k(O,r).
Definicja 2
Kątem wpisanym w koło nazywamy kąt wypukły,
wyznaczony przez dwie półproste zawierające cięciwy o wspólnym końcu, będącym
wierzchołkiem kąta.
![](data:image/png;base64,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)
Definicja 3
Kątem środkowym koła nazywamy kąt, którego
wierzchołek znajduje się w środku koła.
Miara kąta środkowego jest wprost proporcjonalna do długości
łuku, na którym oparty jest ten kąt.
![](data:image/png;base64,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)
Kąt środkowy wypukły
![](data:image/png;base64,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)
Kąt środkowy wklęsły
Przykład 1
Cztery punkty podzieliły okrąg na cztery łuki, których
długości pozostają w stosunku 3:6:12:15 . Oblicz miary kątów środkowych
opartych na tych łukach.
Nazwijmy te kąty środkowe kolejno α,β,γ i δ. Wiemy, że one
również są do siebie w stosunku 3:6:12:15. Ich miary możemy przedstawić w
postaci 3x,6x, 12x i 15x, gdzie x oznacza miarę pewnego kąta. Suma tych kątów jest kątem pełnym zatem:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMEAAAAUCAMAAAADb6kyAAAAAXNSR0IArs4c6QAAAJZQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6Ojo6OjpmOmaQOma2OpC2OpDbZgAAZgA6ZgBmZjoAZjo6ZmaQZma2ZpDbZrbbZrb/kDoAkDo6kDpmkGaQkNvbkNv/tmYAtmY6tmZmtmaQttv/tv//25A625Bm27Zm27aQ29uQ29u22////7Zm/9uQ/9u2/9vb//+2///bDuhZcQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAB/0lEQVRYR+1Va1OCQBRdfISpSWllZAopSIUo9///uc7usuwCmzBT32JndBw8e+855z5grD//2oF9+ifyL6HjjHbXQ1Ho3lxHnFc8xCV0W2NJZOzgjLso0PwKFkdXXcyWzoIx8p/xacbK77WqzL1r5jIB7OgOIx5rYYtlQbK4E3tI1fwKFqfBjnzhZ/aU5g9Iy48lnpE2914sBTB5HdcnrkDGKn+pSzZkZwUlP8UiAHuowPP3iNGbsJaS6QGK3HGaL8tmMdKqbFVExVlmKIC77Uh7THunSn7FjdxD42QuPKXNgULhLVpylkLN1/12o4xkTBMkf7ZynHkd8YMCblUtlg2ZYAwwfTUk+Xw8cITHqqiSX8FClELWI9Yzd/Z4V5KvBroaKPcwBYnDVStEM5OqAb2uRVnbkYwCOTtta4Qxzk+xMBSYFZN9FZv7Rhsn7vAhrSKsNaCQw7oggckmjaz2NuJ9r1joLqpghYPZytwPpgKxsnj7mQirAiWgHakUVJDWLgIS/ARzsBB7SE8d/sy9Nf7A0/Pj52S7LwfBIBiMDixBlaqImgJRxdMcX2EHJPnIGsCxWtZmDUp+ikVcblNuAh/pj6WYlGAUkT/Qa9MgSPKdV0OYCk63mL4pKs2ncBi1I/Fysma1dFHBjxUs4JC4KY9Q0J/egd6B3oHegd878A0Tj0dvz+JTbQAAAABJRU5ErkJggg==)
, zatem:
![](data:image/png;base64,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)
![](data:image/png;base64,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)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAADkAAAAUCAMAAAAA9GVfAAAAAXNSR0IArs4c6QAAAHtQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOjo6OjpmOmaQOma2OpDbZgAAZgBmZjoAZjo6Zma2ZpCQZrbbZrb/kDoAkDo6kDpmkNv/tmYAtmY6tmZmtpCQttv/tv//25A625Bm2/+22////7Zm/9uQ/9u2/9vb//+2///bZUgtRQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAA4UlEQVQ4T+2S6xKCIBCFl9LsolmpRVRqasH7P2G7INhU2P+mM4MDst9ydgHgh3TbcKzmLiIW0KSOWNjo8rp0vMo6mpYAqohxINJOuCpmGtyaBD7VWUukVoWzI1JI4+qEv2UalCCT+DP9RIaNjuqiHF0cLgrO1ySHyrhXBTPSeUmOlBhFw3ygYgGF53JtPb2ebEm1z3rIkFpICrfwkEpQNYNbS+5WLonHrQbxDOqQ6xmusUU+mU62lFpwqNytWLdebo4eFlwmZIXOEowth4v0t8frpN/ob+Rb2Ps+Pa2/RjrwANvdEVDyXxKjAAAAAElFTkSuQmCC)
![](data:image/png;base64,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)
Twierdzenie 1
Jeżeli
kąt wpisany i kąt środkowy są oparte na tym samym łuku, to kąt środkowy jest
dwa razy większy od kąta wpisanego.
Spróbujmy udowodnić to twierdzenie. Podzielimy je na trzy
przypadki.
I przypadek:
![](data:image/png;base64,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)
Założenie:
Niech kąty: wpisany CBA i środkowy COA, oparte na łuku AC,
będą położone tak jak na rysunku.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
AB – średnica okręgu, O – środek okręgu
Teza: ![](data:image/png;base64,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)
Dowód:
Trójkąt BCO jest trójkątem równoramiennym, ponieważ
. Zatem:
, więc ![](data:image/png;base64,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)
Kąt COA jest przyległy do kąta COB, stąd
![](data:image/png;base64,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)
, co kończy tą część dowodu.
II przypadek:
![](data:image/png;base64,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)
Założenie:
Niech kąty : wpisany CBA i środkowy COA, oparty na łuku AC,
będą położone tak jak na rysunku.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEsAAAAUCAMAAADySDD6AAAAAXNSR0IArs4c6QAAAJZQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGa2OgAAOgA6OgBmOjpmOjqQOmZmOmaQOma2OpC2OpDbZgAAZjoAZjqQZmYAZmZmZpDbZrbbZrb/kDoAkDpmkGY6kGZmkLb/kNv/tmYAtmY6ttv/tv//25A625CQ27Zm27aQ27a229v/2//b2////7Zm/9uQ/9u2/9vb//+2///b5jwyoQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABR0lEQVQ4T+2SW1eDMBCENyg13koFL4BtJTRaFYLk//85ZxMQpdaDD3p8MC9wks23M7Mh+qvLnFUfpdmlEGJBVOAjgswfGomfndKxp75A3xA9bojaOKpsfsE/GVl1gC2sQnyH1STnMizJ5jPo1HzzBJjas+oF06fqskoGa74V3HXK6yOirQSCyN5uii9YJhGz5xzlrlmzFPNS872CZXW2hAg9GDLfsWzOSXKY/tTIlNQ1u2CWkSH7Adkl5ZbNEZcnt5cVFX3bcd4oxFHNeb7pip5YFwfulzlGVx+Xm+helivUrmkX6IvPa2DVbgbMchVc3JWOPPKM2tjZ6Yfj5+jGuD0FQUPIA0fPZonUwBq5hK5mdZXdlwOre19tgkwjbMfwdZgCpURUIY8g3fcmlJhXGscTHs0gY+r72hnPJxu/ypoi6L/mJxJ4BXg0JBwYv/xAAAAAAElFTkSuQmCC)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAEwAAAAUCAMAAAAQlCuDAAAAAXNSR0IArs4c6QAAAJBQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgBmOjpmOjqQOmZmOmaQOma2OpC2OpDbZgAAZgBmZjoAZjqQZpDbZrbbZrb/kDoAkDo6kDpmkGY6kJBmkLbbkLb/kNv/tmYAtmY6tpA6ttv/tv//25A627Zm27aQ27a229v/2////7Zm/9uQ/9u2/9vb//+2///btRW4MQAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAABRklEQVQ4T+1STVeDQAzMIkKrpSJq8XuxYJUFd///vzOzAdrSRy+99NAceHlLMjOZhOh8o7mp98W5V6XUkt9aTsK1/GziFb7j2q4TLQvA9AXVI9FPSWTTpHb5Hfo50ddCpdURMJdHtc24ZQBrs9uYdbgc7dWKk4j/muATWGYJ+Cll5qrk8h02V8TBx7a7hxEw91LqI2A6ovY58W7AB7Znsa5Q38/VJSD1QnfAXM6mIkQ1ROnwXaxlsCYOucfwXN4tqfCJx7YPNTH71JjNrKTvOUgHZckvlNkUo3NIYlOvFjKmwQwTdn3dNv/EsxGYxpS+ooJEqR2PCQf2wUi26Ze5gWYe0H3BFdlTsQUT6UPAEOdZD+7MZmwsNoNDnPPJukIlNRkVPE14Zu/f4v64p656xD8s6+AdlvVxMliF1XRxKphYeolzcOAfbp4lf8zO5dYAAAAASUVORK5CYII=)
BD – średnica okręgu niezawierająca się w żadnym z kątów
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Teza: ![](data:image/png;base64,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)
Dowód:
Na mocy pierwszego przypadku otrzymujemy:
– dla kątów COD i CBD opartych na łuku CD
– dla kątów DOA i DBA opartych na łuku DA, zatem
więc
, co kończy tą część dowodu.
III przypadek:
![](data:image/png;base64,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)
Założenie:
Niech kąty : wpisany CBA i środkowy COA, oparty na łuku AC,
będą położone tak jak na rysunku.
![](data:image/png;base64,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)
![](data:image/png;base64,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)
BD – średnica okręgu niezawierająca się w żadnym z kątów
![](data:image/png;base64,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)
![](data:image/png;base64,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)
Teza: ![](data:image/png;base64,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)
Dowód:
Na mocy pierwszego przypadku otrzymujemy:
– dla kątów AOD i ABD opartych na łuku AD
– dla kątów COD i CBD opartych na łuku CD, zatem
, więc
, co kończy tą część dowodu.
Rozpatrzyliśmy już wszystkie możliwe przypadki, co oznacza,
że całe twierdzenie jest już udowodnione.
Twierdzenie 2
Kąt
wpisany oparty na półokręgu jest kątem prostym.
![](data:image/png;base64,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)
Twierdzenie 3
Kąty wpisane, oparte na tym samym łuku są równe.
Przykład 2
Wyznacz miary kątów oznaczonych na rysunku.
![](data:image/png;base64,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)
bo oparty na półokręgu
Kąt α jest kątem wpisanym w koło, opartym na tym samym łuku
co kąt środkowy o mierze 120°.
Zatem:
.
bo jest kątem przyległym do ∢COB
Suma miar kątów w trójkącie jest równa 180°, zatem:
, czyli ![](data:image/png;base64,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)
Korzystające z tej samej własności dla trójkąta ABC:
, czyli
.
Odp. α=60°,
β=30°, γ=60°.
Definicja 4
Kątem dopisanym do okręgu w punkcie A należącym do
okręgu nazywamy kąt wypukły, wyznaczony przez styczną do okręgu w punkcie A
oraz półprostą zawierającą cięciwę o końcu w punkcie A.
Twierdzenie 4
Kąty dopisany i wpisany, oparte na tym samym
łuku są równe.
![](data:image/png;base64,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)
Zadania do zrobienia
1. Dany jest okrąg o środku w punkcie
. Korzystając z danych
na rysunku, wyznacz miary kątów trójkąta
.
![](data:image/png;base64,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)
Odp.
,
, ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAARCAMAAAABrcePAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6AABmADpmADqQAGa2OgAAOgA6OjqQOmaQOpDbZgAAZrbbZrb/kDoAkGY6kLb/kNv/tmYAtmY6tmaQtv//25A627Zm2////7Zm/9uQ/9u2///bxlaYowAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAdElEQVQoU62QzRKCMAyEU7GCQuVXNJS8/2uyGUgP4LF7+TLbzc6kRFn14b3OiPHrIM+J0rlbrz481UFpa1rUOvnxybQ8rnlk1+YN/4f6+5Co9eG4ScZi1tGYTo0VFiCjPfzxpQ3Y92y0qEylcy8mY9ZvJNoAx1IHVeoo/5QAAAAASUVORK5CYII=)
2. Dany jest okrąg o środku w punkcie
. Korzystając z danych
na rysunku, oblicz
.
![](data:image/png;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAoHBwgHBgoICAgLCgoLDhgQDg0NDh0VFhEYIx8lJCIfIiEmKzcvJik0KSEiMEExNDk7Pj4+JS5ESUM8SDc9Pjv/2wBDAQoLCw4NDhwQEBw7KCIoOzs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozv/wAARCADWAO8DASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD2J1XA+UdadsX+6KH6D606mA3Yv90U0Ku8/KKkpo++aADYv90UFFx90U6kPSkA1VXaPlFLsX+6KE+6KdQBGyrkfKOtO2L/AHRQ3UfWnUAN2L/dFNVV3N8oqSmr95qADYv90UjKu0/KKfTX+6aYAEXA+UUbF/uilHQUtICMqu8fKKdsX+6KQ/fFPoAbtX+6Kairg/KOtSU1Oh+tMA2L/dFNdV2/dFSU1/u0AG1f7oo2L/dFOopAR7V8z7o6U7Yv90Uf8tPwp1MBpVf7opEVdv3RTqRPu0AGxf7oprqu37oqSmSfdoAazNx8h6+tO3v/AM8z+dK/QfWnUCI97/8APM/nSBm3n92fzqSkH3zQMTe//PM/nSF3x/qz+dSUh6GgCNWbaPkP507e/wDzzP50qfdFOoAiZmyPkPX1p29/+eZ/Oqesaxp2h2RvdTu47aFP4nPJ9gO5rjl8UeLfFuR4X0tNPsCcDUL/AKsPVUoA7a71C3sIDPeSx28Y6vJIFH61y138UvC9rK0cFzLqEn9yyiMhzTLL4aWU063niW/uddu85/0hsRKfZBxXVWWmafp422djb24XgeVEF/lQBx48e+Ir1d+l+BNQliP3ZJ5Vjz+BFB134j3I/ceFrG3z/wA97nOPyrvKa/3TSA4b+0fihCN0mi6LMPSKdgf1NIPFnjmA4uPAzTepgul/rXdjoKyL3xRplpN9mid726PAt7RfMbPvjgfiRQBzifFG0tpRHreh6ppUg6+ZCXQf8CFb+l+MdA1ohdO1S2nc/wAHmbW/I1Qv7rV7mIPqV1aaBYOduHYSTP7ZPyqfzrG0/wABeHL+/wBW0+5tvN2SRzW9yrbZQrIOQy/7QJoA9B3v/wA8z+dNVmwf3Z6+tcKdA8a+F/m0HV11izX/AJc9Q++B6K/f8a0fD3j+x1O8bS9Ut30fVlOGtbk4Df7rdDTA6ve//PM/nTXZ9v8Aqz+dS01/u0AJvf8A55n86N7/APPM/nTqWkBFubf9zt607e//ADzP50v/AC0/CnUxEe9/+eZ/OkV22/6s/nUlIn3aAE3v/wA8z+dNdn2/cP51LTJPu0AK/QfWnVEyHA+dutO2H++1AD6aPvmk2H++1NCHefnagZLSHoabsP8AfagocffagBU+6K5fxR4x/sy5TRtGt/7R1ycfu7dfuxD+857CqviDxLf3GrDwt4XKyaoy7rm5fmOyT1Pq3oK1vDXhKy8N27mKR7i9uDuubyXmSZvc9h7UAYmleAHub2PWPF94dX1HqsJ/1EHsq98etdwqqihVAVQMAAYAqNkOR87dadsP99qAH01fvNWbqWuabpTCO6vP3zfdgjG+Rvoo5NZ63XiPViRZWq6Vbt/y3u/nlI9RGOPzIoEb9zdW9nA091PHBEvV5GCgfiawm8UPqKlPD9hJqHb7Q+YoB/wI8kf7oNS23hKyWdbrUJp9TuhyJLptwX/dXoBTJ5v+Edu2M7FdKuGyJP4bZz2Poh/Q0hlDWNF1a70mefVNUZyFz9ltT5UQHfJJyxx05FRaOy2Okm00mR0iluUginnQecAfvFuhz1xkV0moWC6tpphS6KB9rxyrhgCOQcdCPas+PwzcmC4e61Vpb+WRJFukgCBGX7vyZwf60AZt7od3qV+lmNQDz6aCYpbuISiRJFAIccAsOxqxpGnpofimOxSRnRtLRAzdWZHbJ/IitXS9LnsWllvL9ry7nOZJvLEYwBgAKM44qnq6mDxXodxuO1hPC3uWUFf5GmB0NYuveFtI8T2hg1O1Dsv+rmXiSM+qtWvsP99qaqHB+dutAjz77f4h+HEipqssms+HchVuwuZrUdt/qPeu8tL611KxjvLKdJ4JQGR0OQRUstuk8TRS/vI3G1kYZBHoa8/vtF1D4d3Mmr+HlkutDY773TM5aId3i+npSGeiUtUtMv7XWNOh1CxufOt51DIw/wA9atbD/fagBf8Alp+FOqLYd/3z0p2w/wB9qYh1In3aTYf77Uiodv32oAkpkn3aNh/vtTXQ7fvtQA9+g+tOqN5EwPmHWl8xP7woGPpo++aTzE/vCkEibz8wosBJXJeNvFFzpvk6JoaC41zUPlhQdIV7yN6AVu6zrVnoekXOpXcoWG3QseeSewHuTXGeDhDZR3XjLxPcRW+oarzGkjcww/woB15pAdJ4P8LweF9J8nf597O3mXdy33pXPXn09K3WdUUs7BVHUk4ArnRr2qamNujaYY4j0u7/ADGv1CfeP1pyeGkvGEuu6jLqbdfJb5IB7bBwfqaAH3Hiu1klMGkW82rTqcEW3+rU+jSH5RTf7N1/VudS1EafAf8Al3sD85HvIeQfpWzGlvbxpFAqRxrwFQYAqXzE/vCnYClpuh6bpKn7HaojnlpCMux9STzV5fvNSeYn94UiyJuPzCgRJUc8cc0LxyorowwysMgil8xP7wpGkTafmFFhmB/wjFzYOX0HVprCM8/ZXUSwj/dB+7+FPz4xi42aRcKO+6RGP4YxW6JEwPmFHmJ/eFKwGCbvxWpwdKsHbsVuCAPzqhrtlfQjS9T1K8WWa21CNtkK7Y41OQwHduo5NdWZE3j5hWN4yXz/AApfCNhvVVdT6EMDTsBvU1Oh+tRwXMU9vHMrDbIgYfQjNOSRMH5h1oAkpsnKkEZB6g0nmJ/eFI8iFfvCgDgbtJvhtrRv7ZWfwzfS/wCkwgZ+xSH+Nf8AZJ6iu/hmjuIUmhdZI5FDK6nIYHoagvba01GymsrtUlgnQpIh6EGuJ8DX03hzWLnwRqcu4QZl02Zv+WsJ5259RSA77/lp+FOqPzE3/eHSl8xP7wpiHUifdpPMT+8KRZE2/eFAySmSfdo8xP7wpryIR94UWEOdVwOB1p21fQUj9B9adSGN2r6CkCrvPAp9Vb+8i06yub2c4jt4jIx9gM0wPN/H1x/wknjfS/CqyyRWNu6y3skYHDn7gOeO3T3rutP8MaVp0gnWDz7kDH2i4PmP+BPQewrhdGsJz4LuvFN0p+3apqEV3k9VjEqqo/75Jr1HIK5HQikA1VG0cCnbV9BSJ90U6gBjKuRwOtO2r6CkbqPrTqAE2r6Cmqq7m4FPpq/eagA2r6CkdV2ngU+mv900AAVcDgUu1fQUDoKWgBhVd44FV9TgWfSruHaDvhdensasH74pxGRg9KAMrwxIJ/DGmscFlt0Rj7qNp/UVpooweB1rD8Gkpor2rH5ra6mjP08wkfoRW6nQ/WgBdq+gprqu3oKfTX+7QAbV9BXHfEnRZLnRU1vTwV1PR2+0QOvUqDll9wRXZ010WSNkcAqwIIPcUAZ+h6nb65o9nqkAHl3MIfHoe4/A1obV9BXC+AS+ha5rPhCYkJaS/abPPeF+cD6Gu8oAbtX0FIirt6CnUifdpgLtX0FMdV29BUlMk+7QA1mfA+Tv607c/wDc/WlfoPrTqBDNz/3P1rjviheSQeDJ7VBtk1GWO0TB5yzf4A12dcH44/03xx4R0t+YXuZJ5F90XK/rQM3dYsTbeBrmzSMAW1j8oB7ouf6VqadM82l2su3O+BG6+qipbyD7TZT2/wDz1jZPzGKzfCU/2nwpYS/9Mtv5Ej+lAGqrPtHyfrS7n/ufrSp90U6gCJmfI+Tv607c/wDc/WlbqPrTqAGbn/ufrTQz7j8n61LTV+81AhNz/wBz9aazPtPyfrUtNf7poGNDPgfJ+tLuf+5+tOHQUtAERZ94+T9aduf+5+tB++KfQI57QC8Gta9bbf8Al7WZRnsyKP5g1uKz4Pyd/WsWD9x48ugeFubGNgPdWYH9CK3U6H60DE3P/c/Wmuz7fufrUtNf7tACbn/ufrRuf+5+tOpaQHB+IGbSvin4e1LZtS/hksnOep6iu53P/c/WuH+LK+T4fstSTiaw1CF429MnBruVYOgYdGGRTATc/wDc/Wmqz7fufrUlIn3aBCbn/ufrTXZ9v3P1qWmSfdoAV+g+tOqJkOB87dad5Z/vt+dAD64PVh9p+Muiw9fs9hLL9MnFdz5Z/vt+dcLdL5PxusnZjibSHjGfUNmgZ3tYHg793o89p/z6XcsOPTDZ/rW55Z/vt+dYHh5PK1TXrbcRi887H++o/wDiaAOgX7op1RKh2j52/OneWf77fnQIVuo+tOqJozkfO3X1p3ln++350APpq/eak8s/32/Omqh3H52oAlpr/dNJ5Z/vt+dV7+za70+4tluZYGmjZBKh+ZCRjI9xQBT1HVZ01CDSdPWNryZPMZpCdsUY4LHHU+gpmlahdrq1xo1/KtzNBEsouETYHB7FcnBH1qrc6HqdrqUepaRNbTTm2W3l+3M/IHIYFRnPrV/S9Ie0muL26m8y9uyDKyfdUAYCr7CkM0j98U+oih3j52/OneWf77fnTEYep/uPGGjXHRZIp4W9ydpX+RrdTofrWB4pTyW0i73tiDUYyx/2SGB/mK3FjPPzt19aAJaa/wB2k8s/32/Omuh2/fb86AJKWmeWf77fnR5Z/vt+dIZyPxTh83wBqLYz5ISX8mFdLpEvn6NYzf8APS3jb81Fc/8AElxD8P8AWSzE77fYAfUkVseHoDF4b0yMu2Us4lPP+wKYjTpE+7TfLP8Afb86REO377fnQBLTJPu0eWf77fnTXQ4++350APfoPrTqjeRMD5h1pfMT+8KBj64LxP8A6P8AFbwrN/z3SaLP0Ga7rzE/vCuG+Jo+zQaNrsR/eabqEZJ9Ebhv6UAd5WBZfufG2qoelxbQyD/gO4H+YrbWaN0V1YEMMg+1YVy6xeO7J9wCz2Esf1IdSP0zSA30+6KdUayJtHzCneYn94U7ADdR9adUbSJkfMOtL5if3hQA+mr95qTzE/vCkWRNx+YUCJKa/wB00eYn94U1pE2n5hRYY8dBS0wSJgfMKXzE/vClYBD98U+ojIm8fMKd5if3hTsBi+M4mk8LXZTh4ykin02up/lmtiCRZoVlX7sgDD6EZqrrKLc6LfQAgl7dwPrtOKh8N3Kz+G9Pctk/Z0U/UDB/UUAatNf7tHmJ/eFNeRNv3hRYCSimeYn94UvmJ/eFKwHFfFuQp4HmQf8ALa4hj/Nq7G1i8i0hh/55xqv5DFcR8QmXU9d8M6CGytze+dMo/uJz/Ou78xP7wpgLSJ92kMif3hSJIm37woESUyT7tL5if3hTHkTb94UWAc4GBx3p2B6Uj9B9adSGJgelYXjLSjrXhLVNPRQZJYCU/wB4cj9RW9TR980AYPgfV01zwhp93/y0WIRSg9VdeCD+VLr37nXtAnA4Ny8TH2Mbf1ArA8OH/hGPiJqnh1vls9TH26z9A38aj+dbnjRCNKtp1do2hvYCHTqu5wpI/wC+qAOgUfKOKXA9Kz/7MnKkf2tejPfKf/E1nyWHiXT8yWOqx6ggJPkXsYDN7B1wB+VAG8wGV4707A9KytJ12DVmkgMUlre2xAntZRh0z3Hqp7EVrUAJgelNUDc1Ppq/eagBcD0pHA2ninU1/umgBQBgcUYHpQOgpaAGEDeOKdgelNP3xT6AEKggggEHg1geCyV8PC3blraeaM/99kj9CK6Cuf8ADf7nUtdtT/DfGVR6KyL/AFBoA38D0prgbelPpr/doAXA9KMD0payvE2tReHvDt7qkv8AywiJUf3m6AfnQBzFiw174u3d3H81volp9mDdvMc5YD3Fd3gelcr8OtGl0nwvFLdgm+1Am7uWPUs/P6CuroAQgUiAbelLSJ92gBcD0psg+XpT6ZJ92hANZnwPkHX1p26T+4PzpX6D606mIZuk/uD86aGfefkH51JSD75oA5Hx/oN5qWnwatpY2atpL+fbMp5cfxJ+Ipk+vw+KfhxPq1uoBWLzJUzzG6HcQfpiuzry/wARWz+BNV1C6SMt4d11GjuFQcWszDAbHoc0hncvrDxiwtoIBNc3cYdVLYCqACWJ9KXRtbOspK0dq6LE5RpCfkZh1Cnv9ao6Fb2mt6DYXyTsJWsxD5kL4IU9vbpWto+mrpGmQ2KymVYRtViMHFAGX4m06d0j1mwQJqVgC8bA481P4o29QRWvYXw1HT7e9gUGO4jWReexGanmUNGynoVI/SsfwfkeGrdCMeWzoB7BiBTEbO6T+4Pzpqs+4/IPzqWmr95qAE3Sf3B+dNZn2n5B+dS01/umgBoaTH3B+dLuk/uD86cOgpaBkRZ94+QfnTt0n9wfnQfvinUCG7pP7g/OsCzLweONQTaMXNpC4Ge6lgf5iuhrAvf3HjTSp+izW88J9zlSP5GgZu7pP7g/Omuz7fuD86lpr/doEJuk/uD86881h5PHvjRNCh+bR9HcS3zK3Esv8KfhW5418TTaVbxaTpK+freo/u7WJf4PV29AKu+D/DUXhbQYrEMJbhyZLmbvLIeSaQzYBcNgRgADgZp26T+4Pzpf+Wn4U6mIj3Sf3B+dIrPt+4PzqSkT7tACbpP7g/OmOz7fuD86mpkn3aAFfoPrTqiaJQB16+tO8pff86AH00ffNJ5S+/500RLvPX86AJarahYWup2M1lewrNbzKVdGHBFTeUvv+dIYlx3/ADoGeU2eiab4L10aRr1sr6Xduf7O1TJVomP/ACydgePau6Hhbyhustc1SH+6DceYg/A1pX+lWOradJY39utxbyjDI/I+v1riRPqfw2uBBfNPqPhh2xFc5LS2X+y3qvvQB0bad4ntx+61y3uh0C3FqE/VahsW8T6RaLBJpNneKpJza3G0nJz/AB4ras7qy1K0iu7G4S4gkGVkjfIIq15S+/50CMP/AISiWAf6foWp2577IfOx/wB8Zp0XjDQC2JdQS2YnhbkGI/8Aj2K2vLHq351E1rBLuWSJHB67lBoALe+tLtN9vcxSr6o4NTNyhrIuPCHh+5ffJpUHmdnVdrD8RVdvCFvEpNpqep2voEumKj/gJ4pDOgHQUtc6NH8Q24zb+IROOyXNsuPzXmgSeKrfmaw0+8HpbzNGT/31xQBvn74p9c5/b13AR9u8OajF/wBcMT/+g05fF2gji5uZLJj/AA3SNGf1piOhrnvEn7q40a76CHUFDH/ZZWX+ZFadtqGm3i7ra9hlH+zKDWZ4ugD+GZ5IyS0MkUoIOcbZFJ/TNAzoawfFfiqz8M2IaQG4vZzttbOPl5n7AD0z3rN8TeNrfTpE0zRojqet3IHlW0ZyI8/xOewpPC/guTT7ltd1+4/tDXZhzK3KwD+6g7fWgCfwh4ZuLJ5td1xhPrl9zK/UQL2jT0Arqqj8pff86Xyl9/zoAX/lp+FOqLyl39+nrTvKX3/OgQ40ifdpvlL7/nSLEu3v+dAEtMk+7R5S+/5014l29/zoAe/QfWnVE8gwOvX0p3mD0P5UWAfTR980nmL6H8qaJBvPX8qLDJaQ9Kb5g9D+VBkGDwfyosAqfdFJLFHPE8M0ayRuNrIwyCPQikWRdo6/lS+YPQ/lRYDg77wNqPh67bVPA959lZjmTTZjmCX6f3TVvSPiVp0sw0/X4X0TU1O1obkEIx/2W6GuvaRcjr19KqanpWl61bmDUrGK6jI6SJnH0PaiwF2OSOVA8bq6HoynINKv3mrhG8A3uiymfwhr1xp4zn7HcZlgPsAelKNe+IOlNi/8NWuqRjq9hNtY/gaAO8pr/dNcMnxX0yEbNT0fV7CYfeRrUuB+IqwnxX8ISDD6hJAT/wA9oWX+lIDsh0FLXJSfFDwZEoI1uGQ46IrE/wAqqt8W/C4OIhfz/wDXK0Y0AdofvilZFcYZQwPqK4X/AIT7WtTP/Eh8G386HgT3RESfl1ofT/iFro2ahqdlolu33lsVMkhHpuPQ0AaPiR/BGkp52txafHJ/CDGDIT7Ac5rjYtJ1TxrOU0GK+0LQySr3E9w+64X/AGYycAV2Wi+APDujyi5a2e/verXV4fNcn154FdMjqBgA4HtTsBj+GfB+j+FbbZp8GZmGJbmT5pJPqf6Vtv8AdpPMHofypryDb3/KiwElLTPMX0P5UeYPQ/lSsAv/AC0/CnVF5i7+/T0p3mD0P5U7CHUifdpDIvofypEkG3ofyosMkpkn3aPMHofypryDHf8AKiwh79B9adTX6D606kMKaPvmnU0ffNADqQ9KWkPSgBF+6KdTU+6KdQA1uq/WnU1uo+tOoAKav3mp1NX7zUAKVDDDAEehqrPpthMp82xtpP8AeiU/0q3TX+6aAKUeh6RH80elWSE91t0H9Ktx28MP+qhjT/dUCnjoKWgBh++KfTD98U+gBKROh+tOpqdD9aAHU1/u06mv92gBaWiigBv/AC0/CnU3/lp+FOoAQ0ifdpaRPu0AOpkn3afTJPu0ANYSYHK9fSnYk/vL+VFFUITEn95fypAJN55X8qKKAHYk/vL+VIRJj7y/lRRQAiiTaPmX8qdiT+8v5UUUANYSZHK9fSnYk/vL+VFFIAxJ/eX8qaBJuPK/lRRQA7En95fyprCTafmX8qKKYCgSYHzL+VLiT+8v5UUUANIk3j5l/KnYk/vL+VFFABiT+8v5U1RJg8r19KKKAHYk/vL+VNcSbfvL+VFFADsSf3l/KjEn95fyoopANxJv6r09KdiT+8v5UUUwExJ/eX8qRRJt6r+VFFADsSf3l/KmuJNvVfyoooA//9k=)
Odp. ![](data:image/png;base64,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)
3. Punkty
dzielą okrąg na trzy łuki, których stosunek
długości wynosi
. Oblicz miary kątów
trójkąta ![](data:image/png;base64,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)
Odp.
,
, ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAARCAMAAAABrcePAAAAAXNSR0IArs4c6QAAAFpQTFRFAAAAAAAAAAA6AABmADqQAGa2OgAAOgA6OjqQOmaQOpDbZgAAZrbbZrb/kDoAkDqQkGY6kLb/kNv/tmYAtmY6tv//25A625Bm2////7Zm/9uQ/9u2//+2///bWzyEIAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAgklEQVQoU7WPWxaCMBBDMyj4AAqCVlvp/rdpQo/FBeD9aKeZOZkU+DPJmeiBZ2PHF5BGq268BtaeQqim5Gokd0VQn6jGXEO9eOYISxEODywte7HpOftu6So0uujBQ/ZdluNp2vSfb85a8/XZ9NWBu7WXiwoKSXzOWVhDirvZJefekQ/hfgcwxbSd6AAAAABJRU5ErkJggg==)
4. W okręgu o promieniu
kreślimy średnice
oraz taką cięciwę
, że
r.
Jaką częścią okręgu jest łuk
?
Odp. ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAYAAAAZCAMAAAAlkq80AAAAAXNSR0IArs4c6QAAAFdQTFRFAAAAAAAAAAA6OgAAOjqQOmaQOma2ZgAAZgA6ZjqQZma2ZpDbZrb/kDoAkDo6kDpmkLb/kNv/tmY6tv//25Bm27Zm27aQ2////7Zm/9uQ/9u2//+2///bgMSJjAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAAAWklEQVQYV32OSxKAMAhDg/Vv/VexlvufU9qpS80GCG8gwGGoYviS78ZCJfMei0uDW3J/WXhDRMn9lAKqXyQvZaL4NnQc2jV6Z89AaIohATGLRpLRQjai+j35ACnuA3cAPEvkAAAAAElFTkSuQmCC)