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Matematyka 2001 

Matematyka

Liczy się matematyka 2

Matematyka 2001

Matematyka 2001. Zeszyt ćwiczeń cz. 1 

Matematyka 2001. Zeszyt ćwiczeń cz. 2

Matematyka 2. Ćwiczenia podstawowe

Matematyka 2. Zeszyt zadań

Matematyka na czasie! 2

Matematyka wokół nas 2

Matematyka wokół nas 2. Zeszyt ćwiczeń cz. 1

Matematyka wokół nas 2. Zeszyt ćwiczeń cz. 2

Matematyka z plusem 2

Policzmy to razem 2

<img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/50969/I%2BaDrUCdbJ3l/Ze5K0P7fQ%3D%3D_84d472744c2af771dff81b35ff8dc6185cf46806584c200e31852fe7c1e224e7.jpg" width="593" height="345"> Punkt C jest punktem styczności prostej m z okręgiem o środku A.&nbsp; Punkt D jest punktem styczności prostej n z okręgiem o środku A.&nbsp; Zatem: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/7262ac1a72c58c489b0abf18804e70e9b60dbde21e7f6398aed4ac4e9005a674_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/7262ac1a72c58c489b0abf18804e70e9b60dbde21e7f6398aed4ac4e9005a674_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/00f215412b257ce12c1480b4dcd98d6d31578d8ac0cc5d65886007353a7f8c9e_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/00f215412b257ce12c1480b4dcd98d6d31578d8ac0cc5d65886007353a7f8c9e_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/eebc99dde55ae9b4dee679c58cc51d6ca90fd391f73befbad53acb60a8b0e1c2_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/eebc99dde55ae9b4dee679c58cc51d6ca90fd391f73befbad53acb60a8b0e1c2_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/83c1212e6d1f4c49b6cea71df2ab07e11aa772357ce4f11267690cdf45873619_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/83c1212e6d1f4c49b6cea71df2ab07e11aa772357ce4f11267690cdf45873619_big.svg" type="image/svg+xml"></object> &nbsp; Kąty&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/f44e64e75f3948e9f73f8dfa94721c4ce8cbb4f265c4790c702b2d41cfbf2753_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/f44e64e75f3948e9f73f8dfa94721c4ce8cbb4f265c4790c702b2d41cfbf2753_big.svg" type="image/svg+xml"></object> &nbsp;oraz&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/be9d587defa1f0c09ef49eb17e206983a5f8f8289e4281860bd0ee5a19592c67_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/be9d587defa1f0c09ef49eb17e206983a5f8f8289e4281860bd0ee5a19592c67_big.svg" type="image/svg+xml"></object> &nbsp;są kątami wierzchołkowymi, czyli mają równe miary.&nbsp; Zatem: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/c53749bb2ddb7626b8f464d80a4e7902111e2dc17a3178f1deb65b9313edf017_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/c53749bb2ddb7626b8f464d80a4e7902111e2dc17a3178f1deb65b9313edf017_big.svg" type="image/svg+xml"></object> &nbsp; Suma miar kątów wewnętrznych czworokąta wynosi 360o. Obliczamy ile wynosi miara kąta&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/8ed3f6ad685b959ead7022518e1af76cd816f8e8ec7ccdda1ed4018e8f2223f8_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/8ed3f6ad685b959ead7022518e1af76cd816f8e8ec7ccdda1ed4018e8f2223f8_big.svg" type="image/svg+xml"></object> &nbsp;.&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/6f192670378dfe5fbdcf8058738279fbd43c32dee25a7b258478ae8bcdcecdcd_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/6f192670378dfe5fbdcf8058738279fbd43c32dee25a7b258478ae8bcdcecdcd_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/7660f9522db83c85deb8c47630e0b8857cfa1552cf7a5745901ab43f46f453f5_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/7660f9522db83c85deb8c47630e0b8857cfa1552cf7a5745901ab43f46f453f5_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/ab7e07f1eefa7440b49a94b7ea6c4354af67e9114345392fecfb47d60f874607_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/ab7e07f1eefa7440b49a94b7ea6c4354af67e9114345392fecfb47d60f874607_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/193062917c9799e84ac72da2d4956b93cb1e5da7b32cc8f536180f689e74c6ff_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/193062917c9799e84ac72da2d4956b93cb1e5da7b32cc8f536180f689e74c6ff_big.svg" type="image/svg+xml"></object> &nbsp; Miara kąta&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/8ed3f6ad685b959ead7022518e1af76cd816f8e8ec7ccdda1ed4018e8f2223f8_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/8ed3f6ad685b959ead7022518e1af76cd816f8e8ec7ccdda1ed4018e8f2223f8_big.svg" type="image/svg+xml"></object> &nbsp;wynosi 120o.&nbsp; <img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/50970/HnhbG1byUtfu6gDFbNk0ww%3D%3D_96e975e8c043f6f752587d0f32795cbcfdb6c1a163ddeaf27cc0d331ecc3e0d5.jpg" width="536" height="304"> Punkt A jest punktem styczności prostej m z okręgiem o środku C.&nbsp; Punkt E jest punktem styczności prostej n z okręgiem o środku C.&nbsp; Zatem: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/7bafdf0ab3ca28e9e6ce34ce1e1b8ee523631270aa77fb991bf38467ec723d5c_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/7bafdf0ab3ca28e9e6ce34ce1e1b8ee523631270aa77fb991bf38467ec723d5c_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/00f215412b257ce12c1480b4dcd98d6d31578d8ac0cc5d65886007353a7f8c9e_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/00f215412b257ce12c1480b4dcd98d6d31578d8ac0cc5d65886007353a7f8c9e_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/eebc99dde55ae9b4dee679c58cc51d6ca90fd391f73befbad53acb60a8b0e1c2_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/eebc99dde55ae9b4dee679c58cc51d6ca90fd391f73befbad53acb60a8b0e1c2_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/83c1212e6d1f4c49b6cea71df2ab07e11aa772357ce4f11267690cdf45873619_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/83c1212e6d1f4c49b6cea71df2ab07e11aa772357ce4f11267690cdf45873619_big.svg" type="image/svg+xml"></object> &nbsp; Kąty&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/f44e64e75f3948e9f73f8dfa94721c4ce8cbb4f265c4790c702b2d41cfbf2753_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/f44e64e75f3948e9f73f8dfa94721c4ce8cbb4f265c4790c702b2d41cfbf2753_big.svg" type="image/svg+xml"></object> &nbsp;oraz&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/be9d587defa1f0c09ef49eb17e206983a5f8f8289e4281860bd0ee5a19592c67_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/be9d587defa1f0c09ef49eb17e206983a5f8f8289e4281860bd0ee5a19592c67_big.svg" type="image/svg+xml"></object> &nbsp;są kątami przyległymi, czyli sama ich miar wynosi 180o. &nbsp; Zatem: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/e6c1188179af96e3a703e24ca4675f0c92babc2c8c2db871fe287a8abab1396c_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/e6c1188179af96e3a703e24ca4675f0c92babc2c8c2db871fe287a8abab1396c_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/1f580a3e68b64625fe34534ffef43acc4b01455bda915999b36383c2cf438f74_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/1f580a3e68b64625fe34534ffef43acc4b01455bda915999b36383c2cf438f74_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/d6feea249f4c97271b0d5724d212fd2ac5707da852e4654805c53e29ab108af0_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/d6feea249f4c97271b0d5724d212fd2ac5707da852e4654805c53e29ab108af0_big.svg" type="image/svg+xml"></object> &nbsp; Suma miar kątów wewnętrznych czworokąta wynosi 360o. Obliczamy ile wynosi miara kąta&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/8ed3f6ad685b959ead7022518e1af76cd816f8e8ec7ccdda1ed4018e8f2223f8_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/8ed3f6ad685b959ead7022518e1af76cd816f8e8ec7ccdda1ed4018e8f2223f8_big.svg" type="image/svg+xml"></object> &nbsp;.&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/357e62d3929d9cdc494bf205343f3ca56bb9e0feb931eca9c4c191f4492d00d6_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/357e62d3929d9cdc494bf205343f3ca56bb9e0feb931eca9c4c191f4492d00d6_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/b1dffa23870c381090f63118a847ff1c65ebca57370e881349cc097ec87a00bb_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/b1dffa23870c381090f63118a847ff1c65ebca57370e881349cc097ec87a00bb_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/4fe458c83682d8f2a4e72cc320d37cc95cf319ddc3f42c893ca999fc345f541d_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/4fe458c83682d8f2a4e72cc320d37cc95cf319ddc3f42c893ca999fc345f541d_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/1335b3cb6437ed01f258994dbbec1c33c651a379e100e8f0004040f93bac5780_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/1335b3cb6437ed01f258994dbbec1c33c651a379e100e8f0004040f93bac5780_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp; Miara kąta&nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/8ed3f6ad685b959ead7022518e1af76cd816f8e8ec7ccdda1ed4018e8f2223f8_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/8ed3f6ad685b959ead7022518e1af76cd816f8e8ec7ccdda1ed4018e8f2223f8_big.svg" type="image/svg+xml"></object> &nbsp;wynosi 60o.&nbsp;

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