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Matematyka poznać, zrozumieć 2. Zakres rozszerzony. Po gimnazjum

Matematyka

MATeMAtyka 1. Zakres podstawowy i rozszerzony. Reforma 2019

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Matematyka 2. Poziom rozszerzony. Po gimnazjum

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Matematyka 2.  Zakres podstawowy. Po gimnazjum

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MATeMAtyka 2. Zakres podstawowy. Po gimnazjum

Matematyka 2. Zakres podstawowy. Reforma 2019

MATeMAtyka 2. Zakres podstawowy. Reforma 2019

Matematyka 2. . Zakres rozszerzony. Po gimnazjum

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MATeMAtyka 2. Zakres rozszerzony. Po gimnazjum

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Matematyka i przykłady jej zastosowań 2. Zakres podstawowy i rozszerzony. Reforma 2019

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Matematyka poznać, zrozumieć 2. Zakres podstawowy. Po gimnazjum

Matematyka. Zbór zadań maturalnych. Poziom podstawowy. Reforma 2019

Matematyka z plusem 2. Ćwiczenia podstawowe. Reforma 2019

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Matematyka z plusem 2. Zakres podstawowy. Reforma 2019

Matematyka z plusem 2. Zakres rozszerzony. Reforma 2019

Matura z Matematyki  2018 - ... Andrzej Kiełbasa. Poziom podstawowy cz. 1

Matura z Matematyki 2018 - ... Andrzej Kiełbasa. Poziom podstawowy cz. 2

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Prosto do matury 2. Zakres podstawowy i rozszerzony. Po gimnazjum

Prosto do matury 2. Zakres podstawowy i rozszerzony. Reforma 2019

Prosto do matury 2. Zakres podstawowy. Po gimnazjum

Prosto do matury 2. Zakres podstawowy. Reforma 2019

Rysunek poglądowy: <img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/79337/wybroFkd8zLG7WQY6%2BGdZg%3D%3D_6555b41fc5d28a8dcd91ed56d7615f18321a3746dae41209905f204e19e23d17.png" alt="" width="255" height="339">

Rysunek poglądowy: <img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/79340/FEMGNmh3cLgilpPm5zXoDQ%3D%3D_26fbc1c05f84c29bec6360845f4a78734c2059fd6226fbb166feed85b0108ffa.png" alt="" width="440" height="302"> a) Z twierdzenia o odcinkach łączących środki boków wiemy, że:

Obliczmy długość przeciwprostokątnej AB: ∣AB∣2=242+322=576+1024=1600 &nbsp;

Rysunek poglądowy: <img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/79342/IE2XPCnKgXXk%2BfpfrXNoJg%3D%3D_5e3b8f5c87bafaa713a1b1c30fb566d9404d6240af49c64376b5b993f291f6c1.png" alt="" width="359" height="252">

Rysunek poglądowy: <img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/79339/9pQybRwnu7TWIC7Dygxtfw%3D%3D_8888817df47db6fc02ecaf9ff1d9114ed98b4cabb887f8d0ea87782dd8abe581.png" alt="" width="495" height="340"> Pole trójkąta ABC: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/7f80f83577a769c1aa76c0a657fb7c3c447ca9021756111d3f4bd064346ad359_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/7f80f83577a769c1aa76c0a657fb7c3c447ca9021756111d3f4bd064346ad359_big.svg" type="image/svg+xml"></object> &nbsp; Pole możemy również wyrazić jako suma pól trójkątów AED, DFC oraz pola kwadratu BEFD: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/8fb170440c7b4da6670b61ae166704bae0b2072b2a52e8b0e629c0e1006b0609_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/8fb170440c7b4da6670b61ae166704bae0b2072b2a52e8b0e629c0e1006b0609_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/8bde33c203bb1fec0b7863c64b6ba8299378366a9964ea14b85d868c7d7535bc_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/8bde33c203bb1fec0b7863c64b6ba8299378366a9964ea14b85d868c7d7535bc_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/2f320b257c8adcbc77442af8d53b47f7912c9319344bac931239c21108f09484_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/2f320b257c8adcbc77442af8d53b47f7912c9319344bac931239c21108f09484_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/976a9940f3bc13ec14cafebe8416e038490fb596164d13f14f91fbe772fdabaa_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/976a9940f3bc13ec14cafebe8416e038490fb596164d13f14f91fbe772fdabaa_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/72d777bfeae6e6e63d1467fae11b182f3907e7ef9a8014507d3a10fe2f01cce2_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/72d777bfeae6e6e63d1467fae11b182f3907e7ef9a8014507d3a10fe2f01cce2_big.svg" type="image/svg+xml"></object> &nbsp; Pole kwadratu: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/c5c9585120c36884671fcc94a90429520297f39d9ad8509c1bdee1a38ce223ea_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/c5c9585120c36884671fcc94a90429520297f39d9ad8509c1bdee1a38ce223ea_big.svg" type="image/svg+xml"></object> &nbsp;

Obliczmy długość przeciwprostokątnej AB: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/0938d64900ead62500297bba06c0e17fa5c02caa59ddc8c05f459f0748a88e17_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/0938d64900ead62500297bba06c0e17fa5c02caa59ddc8c05f459f0748a88e17_big.svg" type="image/svg+xml"></object> &nbsp;

Obliczmy promień R okręgu wpisanego w trójkąt prostokątny, długość jest równa ilorazowi podwojonego pola trójkąta i obwodu tego trójkąta: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/141d0b8bc45dcb1304cad9ee1c2fb4ed611703acf036dda50d1e9c40416e48d5_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/141d0b8bc45dcb1304cad9ee1c2fb4ed611703acf036dda50d1e9c40416e48d5_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp; Rysunek poglądowy: <img src="https://prod.odrabiamy-assets.pl/uploads/content_image/image/80199/lVfuuKH6MKPcU1Dx8eo6Eg%3D%3D_1a80c644148479c8bd68df728dbd6ad7a5cfd8592d711d039a5fdd146b688cf0.png" alt="" width="589" height="451"> Z twierdzenia Pitagorasa w trójkącie AQO2: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/0b4f040cf532eb03e2647f17f893936d72421bab780eff06d18ba0eaddb75228_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/0b4f040cf532eb03e2647f17f893936d72421bab780eff06d18ba0eaddb75228_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/2a322de42d177a86716cf4669c7943e7f4ba8fc62de5b1c3bd8a6402b4c3aa25_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/2a322de42d177a86716cf4669c7943e7f4ba8fc62de5b1c3bd8a6402b4c3aa25_big.svg" type="image/svg+xml"></object> &nbsp; Zauważmy że trójkąty APO1 i APO2 są podobne, zatem: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/fc78abdf516c6183e46fe5f83a16d89c2146d543ff9d433fd270c5806417295f_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/fc78abdf516c6183e46fe5f83a16d89c2146d543ff9d433fd270c5806417295f_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/e26328dece0089cdf4499d99216b11e0d3e950f92e4e2138bc8d89f176417ccb_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/e26328dece0089cdf4499d99216b11e0d3e950f92e4e2138bc8d89f176417ccb_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/f72e4b299ba093a6e50a29405f37d122a379db96a4d4afdc90939302cfa41225_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/f72e4b299ba093a6e50a29405f37d122a379db96a4d4afdc90939302cfa41225_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/b6286de05ea97649e1cb8f7bca07a4574f16abb386807f23358a0e558a453f41_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/b6286de05ea97649e1cb8f7bca07a4574f16abb386807f23358a0e558a453f41_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/da12a0660f691bee833629ada43fc615ce5e8ac48ab03bc3ce136227e511d5ab_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/da12a0660f691bee833629ada43fc615ce5e8ac48ab03bc3ce136227e511d5ab_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/b9d4d7c8dd36fe6673c82f83bc2df9d5792a1baecea481570cf6ccd118ee6e59_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/b9d4d7c8dd36fe6673c82f83bc2df9d5792a1baecea481570cf6ccd118ee6e59_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/7d5759d745d0ceafc241d4ab816062a299e9fd7bae1a6fd5c0fdd635b4fdefbc_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/7d5759d745d0ceafc241d4ab816062a299e9fd7bae1a6fd5c0fdd635b4fdefbc_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/724a48d63a8a0f955c9e21ca01045831b64d0d43abeb0117f5e1517b19b8ac38_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/724a48d63a8a0f955c9e21ca01045831b64d0d43abeb0117f5e1517b19b8ac38_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/6012f24a15a36c66db4b533c33a9ba344d9093a51b7bd6f1440178372d0eea83_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/6012f24a15a36c66db4b533c33a9ba344d9093a51b7bd6f1440178372d0eea83_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/b2cc0d5c05b5410f66c555ea3f8f654f22f0784c19e0f4540ce38d696cea6f98_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/b2cc0d5c05b5410f66c555ea3f8f654f22f0784c19e0f4540ce38d696cea6f98_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/d9bdd3a8be00661d555f5d1214766969c9e3bbd1b969017eef2062290bdf68d1_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/d9bdd3a8be00661d555f5d1214766969c9e3bbd1b969017eef2062290bdf68d1_big.svg" type="image/svg+xml"></object> &nbsp; Z twierdzenia Pitagorasa w trójkącie CRO2: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/73888ca45538754d776af03d1aaa0400aa35f08c4450a37f6bde314441aa72cb_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/73888ca45538754d776af03d1aaa0400aa35f08c4450a37f6bde314441aa72cb_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/4d7ae7226fc9d31649583e46362d4d53b4c449374ddd955623dd488b82cdc65d_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/4d7ae7226fc9d31649583e46362d4d53b4c449374ddd955623dd488b82cdc65d_big.svg" type="image/svg+xml"></object> &nbsp; Zauważmy, że trójkąty CRO2 i CSO3 są podobne, zatem: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/37930350e0f078212b9841f01b94f7fae1f26a643c7dbbf9a83bc00e89ead6bc_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/37930350e0f078212b9841f01b94f7fae1f26a643c7dbbf9a83bc00e89ead6bc_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/53477932ebaf49740002453d3b545279bbe7874baf9ac064d712520731986162_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/53477932ebaf49740002453d3b545279bbe7874baf9ac064d712520731986162_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/b5ae3016cde7ea424f91f6c243357d7554470f081d8855d3ce37db7db3b42c09_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/b5ae3016cde7ea424f91f6c243357d7554470f081d8855d3ce37db7db3b42c09_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/13b8651a92c0d2d546756ad7576208e9d344f7151e8296e5cd2d7ade9dd8f77a_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/13b8651a92c0d2d546756ad7576208e9d344f7151e8296e5cd2d7ade9dd8f77a_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/0cde655c146a72026d2b4dec937a5bed18544d496a23ff2fd4f3b7963db85725_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/0cde655c146a72026d2b4dec937a5bed18544d496a23ff2fd4f3b7963db85725_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/847af2eb1598d7b6f2d1ad64e0e8cce96325c3269937f0654776106f4eb56d08_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/847af2eb1598d7b6f2d1ad64e0e8cce96325c3269937f0654776106f4eb56d08_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/b37650647b95ed75725d0ed0e15dd8ef2a508bbacee4828451d56e365054ff42_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/b37650647b95ed75725d0ed0e15dd8ef2a508bbacee4828451d56e365054ff42_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/66a7c9bf6741bfffeb21e26973ca54853a63ca801879d9dedc3badf3c90fabc6_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/66a7c9bf6741bfffeb21e26973ca54853a63ca801879d9dedc3badf3c90fabc6_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/41ddffd447e1b035f2c296f2c957067832e3c239d1b31aeae317f53d74844261_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/41ddffd447e1b035f2c296f2c957067832e3c239d1b31aeae317f53d74844261_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/69e2ec85cacbca06b11fb94442565612a98c371ac5d17898b3198a32923bc320_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/69e2ec85cacbca06b11fb94442565612a98c371ac5d17898b3198a32923bc320_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/c21c22e4b2d990b5d608c21ebd4e2dccb16f07034262e85bd539dffee4dd37f4_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/c21c22e4b2d990b5d608c21ebd4e2dccb16f07034262e85bd539dffee4dd37f4_big.svg" type="image/svg+xml"></object> &nbsp; Zauważmy, że: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/5b45e834ff8b443720af16a4221430aa8cda799b24c77c478589d298f3284310_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/5b45e834ff8b443720af16a4221430aa8cda799b24c77c478589d298f3284310_big.svg" type="image/svg+xml"></object> &nbsp;&nbsp; Z twierdzenia Pitagorasa w trójkącie LTO2: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/9398a1b54d301f7ce7b2d5df5d2db2063732921719c93e1a5d3e9d5306c2e355_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/9398a1b54d301f7ce7b2d5df5d2db2063732921719c93e1a5d3e9d5306c2e355_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/66ed77732c76ad1a8d738f5300cf958fcd4d2091a80183b3ba8cfa031740478c_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/66ed77732c76ad1a8d738f5300cf958fcd4d2091a80183b3ba8cfa031740478c_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/f3f75610061b88e7198ba4c4cd0358cb018c6c02be5a567bc8026d8a42487df7_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/f3f75610061b88e7198ba4c4cd0358cb018c6c02be5a567bc8026d8a42487df7_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/1870637faada385326b689590848a4f5e1c77645bf53203f0299471536e90819_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/1870637faada385326b689590848a4f5e1c77645bf53203f0299471536e90819_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/bee43d43772c4cc05ca460d7e07b3200d0902bab9fe2ec69b76bb25b0e52667c_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/bee43d43772c4cc05ca460d7e07b3200d0902bab9fe2ec69b76bb25b0e52667c_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/88631cc853c62bd081afdef29e24813284d69e32a1b41ac1794484bc0fd98ad9_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/88631cc853c62bd081afdef29e24813284d69e32a1b41ac1794484bc0fd98ad9_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/1e7179bb2d1e560746930366d21358cc2258b49754c02f3c0cbb509d6f43b294_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/1e7179bb2d1e560746930366d21358cc2258b49754c02f3c0cbb509d6f43b294_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/7b470a5aeb7cbb468cfaaf821da325766ab8d7cf65fe4a37bbd6b7f8b59b2d4a_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/7b470a5aeb7cbb468cfaaf821da325766ab8d7cf65fe4a37bbd6b7f8b59b2d4a_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/5bcb5682de0d4b79f620396ba0e7ec79c33c058cff08722d4cb42b619cb8ebf8_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/5bcb5682de0d4b79f620396ba0e7ec79c33c058cff08722d4cb42b619cb8ebf8_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/30c90fb92b369ff3df2ee4966decfee6c6eedc8fbf5f2a57b80a87bd6db596b8_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/30c90fb92b369ff3df2ee4966decfee6c6eedc8fbf5f2a57b80a87bd6db596b8_big.svg" type="image/svg+xml"></object> &nbsp; <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/b924bf26df25a624b58d673628ade13efbe1d8d024f3192b18a643490cf31380_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/b924bf26df25a624b58d673628ade13efbe1d8d024f3192b18a643490cf31380_big.svg" type="image/svg+xml"></object> &nbsp; Zauważmy, że: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/802d5aa0cf058b8e13a392bdb894926f7c83a8b20db2d8f21a4ee349d778a6c1_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/802d5aa0cf058b8e13a392bdb894926f7c83a8b20db2d8f21a4ee349d778a6c1_big.svg" type="image/svg+xml"></object> &nbsp; Zatem jedynym rozwiązaniem jest: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/eeaa77734f942371dc6550d75cd488c7b8b6195c3528051750087e3593fe46c1_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/eeaa77734f942371dc6550d75cd488c7b8b6195c3528051750087e3593fe46c1_big.svg" type="image/svg+xml"></object> &nbsp; A więc możliwe długości promienia&nbsp;r, w zależności od położenia okręgu&nbsp;to: <object class="math small" data="https://odrabiamy.pl/api/v3/math_formulas/4b245c971092e246a5a24a55f6d98b6c11bc74570eee92924862c9014590afe6_small.svg" type="image/svg+xml"></object><object class="math big" data="https://odrabiamy.pl/api/v3/math_formulas/4b245c971092e246a5a24a55f6d98b6c11bc74570eee92924862c9014590afe6_big.svg" type="image/svg+xml"></object> &nbsp;

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