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<p style="text-align: justify;"><span style="color: #000000;"><em><span style="font-weight: bold;" data-mce-mark="1">Es defineix la bisectriu d'un angle com el conjunt de punts equidistants dels segments que determinen l'angle.</span></em></span></p> <p style="text-align: justify;"><span style="font-weight: bold; color: #003300;" data-mce-mark="1">En el triangle de vèrtex «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/mi»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»B«/mi»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»C«/mi»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math», quina és l'equació explícita de la bisectriu de l'angle A?</span><br style="font-weight: bold; color: #006600;" /><br style="font-weight: bold; color: #006600;" /><br /><br /><br /></p>
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<p><span style="color: #003300;"><strong>Gràficament:</strong> </span>#G1</p>
No, case is unimportant
Yes, case must match
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Answer 1
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Answer 2
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<div style="text-align: justify;"> <span style="color: #0000ff;"><strong>Primer calcules l'equació CARTESIANA (de la forma ax+ by + c = 0) de la recta AB que és una recta que passa pel punt A i que té, per vector director, el vector AB.</strong></span></div> <div style="text-align: justify;"><span style="color: #0000ff;"><strong>Després calcules l'equació CARTESIANA de la recta AC que passa pel punt A i que té per vector director, el vector AC. </strong></span></div> <div style="text-align: justify;"><span style="color: #0000ff;"><strong>Agafes un punt qualsevol P(x,y), i escrius la seva distància amb l'expressió</strong></span></div> <div style="text-align: justify;"><span style="color: #0000ff;"><strong>«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»,«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mfrac mathcolor=¨#0000FF¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«msub»«mi mathvariant=¨bold¨»ax«/mi»«mi mathvariant=¨bold¨»P«/mi»«/msub»«mo mathvariant=¨bold¨»+«/mo»«msub»«mi mathvariant=¨bold¨»by«/mi»«mi mathvariant=¨bold¨»P«/mi»«/msub»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«msqrt»«msup»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mfrac»«/mstyle»«/math»</strong></span></div> <div style="text-align: justify;"> </div> <div style="text-align: justify;"><span style="color: #0000ff;"><strong> a les dues rectes AB i AC i les iguales<br /></strong></span></div> <div style="text-align: center;"> <div style="text-align: justify;"><span style="color: #0000ff;"> </span></div> <div style="text-align: justify;"><span style="color: #000080;"> </span></div> <div style="text-align: justify;"><span style="color: #ff0000;"><strong>Atenció, com que són distàncies, apareixen valors absoluts. Cal fixar-se en el gràfic per escollir la bisectriu de l'angle i no la seva perpendicular.</strong></span></div> </div>
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