[justify] No estudo dos triângulos, o baricentro, o ortocentro, o incentro e o circuncentro são pontos de grande importância, pois cada um deles possui propriedades geométricas específicas que auxiliam na resolução de diversos problemas. Esses pontos, chamados pontos notáveis, são oriundos na intersecção das cevianas e das retas mediatrizes do triângulo. A seguir, veremos mais sobre cada um desses pontos.[/justify]
É o ponto de encontro das três [b]medianas[/b] do triângulo. [br]- Divide a mediana em duas partes, a parte que vai do vértice até o baricentro tem valor igual ao dobro da parte que vai do baricentro até ao ponto médio do lado que a mediana é referente;[br]- Ele é o centro de massa do triângulo, ou seja, o ponto de equilíbrio;[br]- É interno em todos os triângulos.
[justify] É o ponto de encontro das três alturas do triângulo.[br]- A posição do ortocentro varia conforme a classificação dos triângulos em relação aos lados. No triângulo:[br]Acutângulo: está localizado internamente;[br]Retângulo: coincide com o vértice do ângulo reto;[br]Obtusângulo: está localizado externamente.[br][/justify]
É o ponto de encontro das três bissetrizes internas do triângulo.[justify]- O incentro é o centro da circunferência inscrita no triângulo;[br]- É equidistante de todos os seus lados, isto é, as distâncias entre o incentro e os três lados do triângulo são todas iguais, e essa distância corresponde ao raio da circunferência;[br]- O raio da circunferência inscrita é perpendicular ao lado do triângulo;[br]-É interno em todos os triângulos.[/justify]
[justify] É o ponto de encontro das três mediatrizes.[br]- É o centro da circunferência circunscrita ao triângulo;[br]- A posição do ortocentro varia conforme a classificação dos triângulos em relação aos lados. No triângulo:[br]Acutângulo: está localizado internamente;[br]Retângulo: coincide com o ponto médio da hipotenusa;[br]Obtusângulo: está localizado externamente.[/justify]
Explore os pontos notáveis no [i]applet.[/i][br]- Marque/desmarque as caixas para fazer aparecer/desaparecer os elementos descritos. [br]- Clique e arraste os vértices do triângulo para alterar sua forma.
[justify]Para fazer um experimento em sala de aula, um professor utilizou uma placa rígida uniforme com formato de um triângulo escaleno e um pouco maior que um livro escolar. Assim, apoiando seu dedo indicador em um ponto destacado na superfície da placa, o professor conseguiu equilibrá-la e mantêla paralela ao chão.[br]Esse feito ocorre pelo fato de o ponto destacado sobre a superfície ser:[/justify]
[justify]Duas guaritas estão localizadas em um terreno no qual é desejado construir uma estrada retilínea e pavimentada. O projeto estabelece que qualquer lugar estrada esteja sempre a uma mesma distância das guaritas. Considerando este um problema de geometria plana, em que as guaritas são representadas por pontos e a estrada por uma reta, a estrada é, em relação ao segmento que liga as duas guaritas:[br][br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARMAAACeCAYAAAAR8O4KAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAAEnQAABJ0Ad5mH3gAABlzSURBVHhe7Z0JcNXl1YcPi6SIQCggIayCgCirgii4FOI2uKJiVRywLVRBhgJaKn6OVioWKqLggkuXqVVbV2SQtaLIJgpllcUQNYAsCYsgIWyCX56T+w8XSGJCbkJu7u+ZuRPue/9bgPd3z3vOec8p92MWJoQQRaR86KcQQhQJiYkQIiJITIQQEUFiIoSICBITIUREkJgIISKCxEQIEREkJkKIiCAxEUJEBImJECIiSEyEEBFBYiKEiAgSEyFERJCYCCEigsRECBERJCZCiIggMSkChw8f9pcQogyIyXfffWcjR460FStWhEZKjjfffNMmTpwoQREii6gXk2+++cb++c9/2ubNm0Mj2ezfv9/69Onjkz2SpKSk2JgxY+yBBx6w++67zz799FM7cuRI6FMhYpeoF5PWrVvb+++/b127dg2NZJORkWEffPCBnX766aGRyBAfH2+XXXaZPfzww6byuUIcJerF5LTTTrNzzz3X4uLiQiPZLF261BISEqxhw4ahkchQq1Ytu/DCC11UhBBHKZCYbNmyxSZPnmwff/yx/fDDD5aZmZlj2mMBfPTRR27u81kAf2YJcuDAgdDIUfbs2ePnzJgxw6/FkiTc77BhwwZ75513/Cf3+frrr23SpEm2atWqnPtyfe45bdo0O3ToUM4YIvLJJ5/YW2+9ZVWrVvVlCWPcI5xvv/3Wrzlnzhy/9/fffy9LQ4gikK+YMMmmTJliw4YNs7p161rt2rXtiSeesJtvvtkn38GDB+29996zM844w5599lmbOXNm6ExzAejVq5elp6eHRsyFYOHChTZkyBCrWLGi1atXzyZMmGDXXXedffXVV34MxyMQlSpVst/+9rd+/0BEhg8f7sfxXByzb98+//yvf/2rn8v4xo0bXWTmzp3rz8vxCEe5cuX8GMTt3//+tz9v06ZN/f1jjz1md955p38uhDg58hWT2bNn26hRo9zReMEFF1irVq1s69attmnTJp+cs2bNcrO/ffv2tnLlSrdEApYvX27btm1z0Qgg4oIw9ejRwy655BK/HlZFcnKyVahQIecYhOuss85ySwjr5Prrr7e0tDS3LhCZL774wi0ifBeMr1u3zs9lqXPDDTe4OP3sZz/z5x48eLCfHyyDEL/x48dbv379/P5JSUm2aNEiFyYhxMmTp5ggGmPHjnWh6NixY843+/bt291nwOTEEujSpYt9/vnnbqW0aNHCjwGWGggQVgtgyWAN/PznP7crrrjCypfPvvXu3bvdiRr4IHbs2OFCs2bNGmvevLldffXVPn7HHXfY3//+d6tfv76LykUXXWRr1651IeJ5AliqIC67du06Zhw49plnnrHbbrvNmjRpEhrNDi9369Yt9E4IcTLkKSZ8W0+fPt1++ctf5lgNfHsvXrzYOnXq5BYCFkCVKlXc94A1wTgw2bEq2rZtmxNNYYK//vrrfr3ASsDHMW/ePBes6tWr+xifIzhYRYzjRAU+R0h4Fu6DYxW/C8sULI8ABA6rqHHjxn6dAJZJ+Gj47JZbbjlGzPCrdOjQIUcwhRCFJ08xYYLhwCRSEoDvgmULFkMwGbFUcHBiTXA8YDEwedu1a+fHMcGDpQhWSEBqaqpbEIwhEhwHiNayZcv8PohVbuC4Rey6d+9ulStXznH+YiFhKfE8gKXCUoprL1myxJdP4REeRBMhbNCggR8TOHiFEIUjTzEhgtOoUaMcK4JJho+kZs2a1rJlSx8DxAC/xjXXXBMayfZ7YJHgk2BpgZDgGMXhWaNGjdBR5pMbzj//fHfYsrSB1atX2969e90CyctaQIg4/8Ybb3QHK1EZQEwCcQOWV1gkwLPyTAGIx9SpU/33xJLBcYsPRghRePIUE3wSWBV8swd+CLJJ8TUQJQlg8mIlBBYEIsCk5D1LFJYiLFHatGnjghSEX5nYRH8YYzL/97//dQHic8SEiY7I5AX3QJwQgc8++8zzTWD9+vXufOXeXIMQMc/M74JPJziO+2Bp8XznnHOOn8PSKrCu8oNzsYT4KWtGiGwq/DGL0J+PoU6dOm5NMGlwipJNOn/+fE9Rx7EagADgd8ACwY/CsoFzGGNi4tMg6oL/gusx8bAWsF6wcnD04nwl9+TKK6/0yUmOCZOfe+UFyysiSAgb1ssvfvELFwqWYTwnz89SDcFBlLgeyxtEi2UN1gz+k8TERI86ER1iSRfuRM4NLBcECD8RvwO/K/fnfK4V+JeEiDXKZX275pmphfXApOMQJhxREKI05513XuiIbHbu3OnhWiI31apV80nLUgM4NojoIBxcj4mN5cCEZ0LisGUiY8EgNsFy5/j7hINFhDOYa7HsChy4nP/ll1+6OCFSPAtWR0DwWeD74XfjOogiDt/wUHZuIKz4hI7/a8Nvg8P5p84XoqySq5ggDvgkmMyBz+Tpp5+21157rcBLASFEbJGrz4SMUpK9EBRgScF2+3vuuScn1CuEEOHkKiYsGZo1a+Z+DyIhjzzyiD344IPWt29f+QSEELmS6zInSHHHZ4K/A8ciafNK6hJC5EW+DlghhCgoeeaZCCFEYZCYCCEigsRECBERJCZCiIggMRFCRISojeaQNk/FNzb5zZ0733bvzrBWrVr4BkVqk4Sn0Aship+oFROKLz322Chbt66yxcd3sYoVq9iePcl26NBC69evu/Xv3/+Y3c1CiOIl6sSEx/3f//5n9977gB08eLslJva0SpVq+mdHjhy0vXu/yRKYoXb77a1s1KiR2ngnRAkRdT4T6qWMGzc+62eSNW58b46QQPnylaxq1RbWrNkYe/PNBV6KQAhRMkSdmFA+YO7cFKtT5+bQyImccUaLrFeSTZs2/YRSAUKI4iHqxIR6KJmZ1SwurlZo5ETKlSufZaF0sJSUdW7JCCGKn6gTE6I0P/54KOt1tANgbhw+nOlWCZXeVFZRiOIn6sSE6mzx8Xtt//6toZETQWh27ZrnFdtGjhzpZRSoDSuEKD6iLppDiceHHvo/mzTpgLVsOdadruHw6+zcOc+SkwdY69a1vYQCtWHPPPNMb8pFFX1qwAohIktULnN+97tB1qLFBlu16n7bs2dt6BOaeu2xtLSplpo6xO6/v5fdfffdXiCaItUkuFFMmjq0QojIE7VJayxhHn98tM2atcbi4pplWR/xlpGRnGWJ7LQRI4Z6z2GKPFMAmir0FMLGQqFpOkWvhRCRJWrFBKgIR7N08kmoCkdvHroI0kLjeHDCElYOqtjnBhXvsWKwflRVTojCEdViEmnY5/Phhx96E3N6A9EHSAhRMCQmYQwfPty7/AE1b2nMTh9k+hMrLV+I/JGYhDFhwgRfMtFxEGjwhajQEfDSSy/1PkKMCSFORGISBv4SQs/0QP7888/tq6++8vdAiw96EiclJbm40O5UCHEUiUkeBC1PaZCOL4WewoBlMnToUO+fLIQ4isQkH/irIWK0ZcsWr5+CtUJEaNy4cbJMhDgOiUkhYJNhenq6NyhXZ0MhjkViEmE2btzoSyMEp0GDBurNLGIGiUkEITGOBu+8SI5DUDp16uQOW7JxhSjLSEwiSEZGhr366qseXsa3AohI/fr1PQpEdi6hZiXDibKIxCTCUD9l2bJltnjxYnfYfvfdd6FPzOrVq+eV86mgzwZEJcKJsoTEpBjgr5R9PuxQRlCIBG3fvt1zVtjzw0bDa6+91m655RbffChEWUBiUgKQs8LO5Tlz5tjq1at9bODAgZ5VK0RZQWJSguzevdutFZZBV199tcXHx4c+ESL6kZiUQjIzMz37tkmTJu6wFSIakJiUQlauXGmjRo1yIencubOn7lOjBf+K6qyI0orEpBTyj3/8wyZOnBh6Z56zQv1aokDnnnuuValSJfSJEKUHiUkpZPPmzbZ06VLfvUwKP/uDAFFp2LCh56xQvIli2UrrF6UFiUkphvAyfZUXLFhgK1asOCZnJSEhwbp372433XRTaESIU4vEJArYt2+f17oNykrSpZDUfYpm9+3bN3SUEKcWiUmUQRW4hQsXurDcddddXlJSiNKAxCQK4Z8M6yQuLi7PDNrgmMBZqyiQKG4kJmUUSiGMHj3aNxl26dLF69eSJKcatqK4kJiUQfCnTJ8+3f72t795JAgLho2FlEKgPapqrIjiQGJSBuGflGLY06ZN8yjQtm3bXGCCTYYdO3a0q666yncxV61aNXSWEEVDYlKGQUBSUlI8o3bGjBnH9FmuUaOGNW3a1MPL9AbCehGiKEhMYgBEhfAyGwxp3k6YOchZoRLcoEGDZKGIIiMxiTEQleTkZK9TS4i5Z8+eXltFiKIiMYlB+CenDxClJWnSnp9DlvAyxyhtX/wUEhORLy+//LIvgdi5jMNWiLyQmIg8SU1NtSFDhvifiQK1atXKQ8u08GDToRLhRDgSE5Ena9eu9VwVIkL0YQaiPi1btrSLL77YQ8zUWZGoCJCYiDwhCsReIHJWSIJbt26dR4H4L0O7Dlqksvwhw5bSCPKrxDYSE1EgcNgSUqYnEG08NmzYEPrErE6dOvb00097fRURu0hMRKFAVLBOaOFBtX1EhQpwAwYMUNuOGEdiIk4ahIXiTXXr1vVljohtJCaiWMHvQoIcPpZzzjnHSyJo53LZRGIiipX09HT7y1/+4hEh9gJdcsklvnuZ8LJEpWwhMRHFypo1a1xMdu3a5eFlIj44bOm53LVrV0+EI9ys8HL0IzERxQ67lT/55BP3rxBmDqrtIyxBI/e2bduq4ViUIzERJQJWyY4dO9xSoSg2CXFU3+e/H3t/mjVrZn369LHmzZuHzhDRhsREnBIQlXnz5tmSJUu8TxCFsUeMGOFp+yI6kZiIUwahZZqMUQ0OZ+x1110X+kREIxITERXgd6FkAvksqgpXOpGYiKjg+eef90px9Fqmfi0FsitWrBj6VJQGJCai1JOWlmaPPvqo+1aAMDIO227dunkUiAxc5ayceiQmotQT1K9lLxB7gsJDy40aNfIm7pdffrlS+k8xEhMRFfDflPAyVsqsWbN85zKWCuFlLBX8KO3bt/fwcmJiYugsUZJITERUgpDQwoNkuC+++MLH2PfDcog9QKLkkZiIqIVNhAcOHPA6KzNnzvQSCL1791bbjlOExESUCVgCUUk/v6Q3fC/4WdjBLCKPxETEBFgxNCCjZSobDPGvsOFQOSuRQ2IiYgKsEtL1V61a5e8TEhI8ChRsMhRFR2IiYgKiPpMmTfJCTaTw79+/36NAOG2ps5KUlOQ9l2nhoWS4k0NiImKKjIwMF5Tly5d7e1REJoAdyyx/WAYpvFx4JCYi5uC/PMseimHPnTvXxWX37t2eDIdVMnjwYG/hIQqHxETENDhmSYRbtGiRC8v27du9bUd8fHzoCFFQJCZCZME02Llzpzcdo7ZKXiA+WDCEl1Vq8lgkJkIUApy3kydPtjZt2ng0iCpxIhuJiRAFBKvk1Vdftffee8+7F2LB0BqVF1EhEuJi2VqRmAhRQHDaIiQkv7EkCiD5jXwV2nggMLGaYSsxEaIQkJ+SmprqlfY/+ugjb5VK+Uk488wzrUmTJnbttdf6ZsOC+FWwdpiCWDXRjsREiJOEMpKfffaZF8b+8ssvfW8QICC33nqr3XHHHXkmwLHrmTIKnEeuC8We2rVrF9XV+SUmQhQRclTYuTxjxgxbunSpV30bOHCgXXzxxSdYJkw3CjyNGPG4rV6dmfV526zj47KsmxWWmLjXhg0b7JZNNDaBl5gIEUHoDUR9FSI9OGmPh3yWHj1+bTVr3mcNGvw6S0iO+lfS06dnWSp/sOee+4P16nVnaDR6kJgIUUKQEDdgwABbs6azNWrU3y2ScI4c+cHS0qZkjY+z1157yZc+0YSq8ApRQtAaddGizVa//t0nCAmUL1/R6ta9Mcu6SfAKctGGxESIEmL9+vV26NBZVq5c/jVUKlVqZykpKTmFs6MFiYkQJQRhYLOfTmorV6586NjoQmIiRAnRuHFjq1gx1X788UBoJHcOHFhmZ599dtRFdCQmQpQQZMe2a1fTtmx5M8vyOFpHJeDIkcOWnj7Dqlff5Nm00YbERIgSgrT7YcN+b9u3v2CbNr2RJR7H+kR27JhtKSkP2cCBvb0NarSh0LAQJQi+kI8//thGjnzS1q8/zSpUuMAjOwcPLrMaNbba4MF9rWfPnlG5G1liIsQpYOPGjZ6Gv3bt2px0+gsvvNBatWoVOiL6kJgIcQphkyBTMBrT549HYiKEiAhywAohIoLERAgRESQmQoiIIDERQkQEiYkQIiJITIQQEUFiIoSICBITIYQdPnzYDhzIfzfzT6GkNSFKEWvWrLGnnnrKyzuef/75odHsQtS02SBTNq+K9ycDGbjsFfrggw/8fUZGht12222WlJRU6PvIMhGiFEGFNRp8UeE+nK1bt9o111xjU6dODY0UHSq5vf76697ydNy4cTZ27Fi79NJL7Ve/+pU999xzLl6FQWIiRCniiiuu8IlMD51wVq1aZbt27bL69euHRooOVgiNxC6//HJ/TyMwrBKe4dlnn3UrqTBITIQoRVSuXNkSExND77KhbAEdBGmdEcldxexcpnfyQw89FBoxO/300619+/b29ddf+6swVPhjFqE/C1HmYWKuXr3a3n33Xe9xU7duXTfn4+KyizyzxMD057OmTZv6GOCzoMFWjRo1TvAlbNq0ySZPnuzd+Ro2bOjXC69HQq+cd955x0WievXqNmfOHPdRcAwFkwArYdKkSV6SgPtyDzoEzp4925t2TZw40Z+d87dt2+YlIAPwe6xcudJ/J7oMck2uhzD9FN9//70vn1q3bh0aMW8mRnkEOhLS5rSgyDIRMQOd90aPHm3jx4+3Hj16WIMGDezBBx/0DnobNmxwUUBIunTpYo8//ri3/gxgcv3mN7/xCvMBmZmZ9uKLL9ojjzziZRY7dOjg5+F3WLFihR9DQ64lS5ZY7dq1rVevXvbyyy+7hVGlShXv+sd9Wb688cYb1qJFC3vrrbfsP//5j59LN0B8J4jH8uXL/R4IB+cGbNmyxR599FEXp7vuustF795777V77rnH+yDnB72RJ0yYYLfffntoJPt3os0Gzt/zzjsvNFowJCYiJmAS/utf/3IfwZ/+9CdLSEjwb10EhIkeHx9v8+fPd0HgWCwTJnkAFkKtWrV8AgZMmzbNXnjhBReTRo0a+YvwKmIRWBzTp0+37t27+59xdGIJYQWkp6f7kgVLB2uE8Zo1a1paWppPaGDJgf8CcUNYevfu7dZCx44d/fN9+/a5bwOn7aBBg9xqueyyy9zywgoKF53cCMQqaGGKEM2aNcstLAQp3PopCBITERPQAOvPf/6zT8ZAEPjmpsseFc6YuEyetm3b2qeffurjQVFnlgILFiywTp06uegAy6GHH37YLZzAKcrkRjDatGnj90BY8D8gQjhQsTyuvPJKD+8OGTLEIyhVq1b1JQ1OUESF47p16+bXC8AqatmypYtNOFhOr7zyivXv39+vA1gqQJ/jSpWOth4tCPhQnnjiCRs2bJj16dNHoWEhcgM/AN/CTO4AHIwsIRATJg4/mehYHORZBN/sNCXnhekffIuTm4HgYDUQBQEmMscFDcvxw3AdRIXICOcHvhTuE1RXwxqqVq2a+0U4FyslHIQMa4ZjwsEPw7FNmjQJjWTnqXA/RLEw4Gt58sknPZrTr1+/nN+pMEhMREyAD6N58+a+vAFMeiYekwiLI4B6rCxpbrjhBn/PcYgOyxKsCpyigTO2Xr16xywF8KfwwspgqcJxsHnzZr9X586d/X1uIEwffvih3XTTTS44OFAB6wmLBSHC0iA3hGcGHLOMBxYLDlp8K4ggvysWVUHgWQlHYxHhx+F8ln9YKoVBYiJiAiIsTDr8GcCkxEfC8iHct8Ak4phwkUAI6HnDUgLrAZFgouJrCcQJcLayvOE1ZcqUnPR0rokohFtFxzNz5kwXCyyT1NRUfzbg3lhUOEOxdhAxfCTAsgrLJIjaIDILFy70+2BZEN35KfAPvf/++y4++HYCawmnMc7hwiAxETHB9ddf79/AvBAWlg5vv/32Cf4JJlcQJgYcoiyRcJZiPWChANYMYoGlgkWARRJMSiY1ghBYJvhg8KME/pbcWLZsmQsYSxYsI0LMwLKJJRjjZMEGFhHw7Igi9+cnS6/Fixf7sik5OdnH8oPPiUa99NJLHq4ePny4DR061F9ElQrrc1GeiYgJmJxYCExIvtn5SaRl8ODBx+STEF3hOCY3QsESg1adiANChIWAlcIYUQ/EBucu51x00UV+bULQHIewYE0QfsVa6Nq1a56+CCwXckXYcMezBksv/CRYGwgGz4DlElhNPAcigHhhwSBetMxYt26dCx/LMpy/ecEyZsSIEb4MQ3z4fYIXkaFbb701XwE8Hm30EzEB/82xSBAIJjghUELEWCfhiVkch2gQrcFCYQnBNzTvWQIwuYNvbCYxx3I9lkaME1LmPZMxsHAQLq7DuXyWG1g5CAD3QNCC5QZgDSEmXI/rBvt2GEOE+Ml1mfj4fBjjWK6TnyM1uGdu8LvklqCXHxITUaZhovGty/r/qquu8jGWMjgaEQLyRAI/iiga8pmIMg3WyJgxYzzTFXBakvrOUoAljoQkcsgyEWUanIxsZiO8SxIaZj1OTRyy+UVXROGRmIgyT+BHwErBB0CIOBobg5d2JCZCiIggn4kQIgKY/T+cKIwpu4okhAAAAABJRU5ErkJggg==[/img][/justify]
[justify]Em um parque de diversões há três estabelecimentos: um posto de primeiros socorros, uma barraca de pipoca e um guichê para compra de ingressos. Deseja-se construir um banheiro de modo que ele esteja a uma mesma distância desses três estabelecimentos. Considerando este um problema de geometria plana, em que os estabelecimentos são representados por pontos e que construímos um triângulo a partir desses três pontos, o ponto que satisfaz ao objetivo é 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[/img][/justify]