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ÊÁѤÃÊÁÒªÔ¡ | ¤ÙèÁ×Í¡ÒÃãªé | ÃÒª×èÍÊÁÒªÔ¡ | »¯Ô·Ô¹ | ¢éͤÇÒÁÇѹ¹Õé | ¤é¹ËÒ |
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#1
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¤ÇÒÁÂÒÇ´éÒ¹¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁ´éÒ¹à·èÒ
¡Ó˹´ P à»ç¹¨Ø´·ÕèÍÂÙèÀÒÂã¹ÊÒÁàËÅÕèÂÁ´éÒ¹à·èÒ ABC
¶éÒ¤ÇÒÁÂÒǢͧ´éÒ¹ PA, PB áÅÐ PC à·èҡѺ 5, 7 áÅÐ 8 ˹èÇ µÒÁÅӴѺ áÅéÇ ¤ÇÒÁÂÒǢͧ´éÒ¹ AB à·èҡѺà·èÒ㴠ú¡Ç¹¼ÙéÃÙéªèǤԴãËé˹èͤÃѺ ¾Í¡Ó˹´à»ç¹ÊÒÁàËÅÕèÂÁ´éÒ¹à·èÒ àŨ¹»ÑÒàŤÃѺ ªèǼÁ˹èͤÃѺ ¼Á¾ÂÒÂÒÁàµçÁ·ÕèáÅéÇ ¢é͹Õé¼Á¤Ô´äÁèÍÍ¡¨ÃÔ§æ |
#2
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ãËéãªéÊٵáÒÃËÒ¾×é¹·Õè heron s.o.s http://en.wikipedia.org/wiki/Heron's_formula ¨Ðä´é ¤ÇÒÁÂÒÇ´éÒ¹ AB »ÃÐÁÒ³ 664.677 ˹èÇÂ
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#3
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ÍéÒ§ÍÔ§:
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#4
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ÍéÒ§ÍÔ§:
23 ¡ØÁÀҾѹ¸ì 2009 12:49 : ¢éͤÇÒÁ¹Õé¶Ù¡á¡éä¢áÅéÇ 3 ¤ÃÑé§, ¤ÃÑé§ÅèÒÊØ´â´Â¤Ø³ ¤Ø³ªÒ¹éÍ à˵ؼÅ: äÁèÍÐäà ¾ÔÁ¾ì¼Ô´¤ÃѺ |
#5
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¶éÒ¶Ö§¢¹Ò´ºÍ¡ÇèÒ confirm ¡ç¤§äÁè¡ÅéÒÇèÒ¼Ô´áÅéÇÅФÃѺ ¼Á¡çàª×èÍÇèҤسªÒ¹éÍÂÃÕºá¹è¹Í¹ à¾ÃÒд٨ҡ¡Òõͺ¡ÃзÙéµèÒ§æáÅéÇ µéͧºÍ¡ÇèÒäÁè¸ÃÃÁ´Ò¨ÃÔ§æ ËÃ×ͺ͡ä´éàÅÂÇèÒà»ç¹»ÃÐàÀ·äÁèµÔ´´Ô¹¨ÃÔ§æ (¼ÁËÁÒ¶֧¤ÇÒÁÃÙéÃдѺà«Õ¹àËÂÕºàÁ¦)
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#6
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à¾ÔèÁàµÔÁ : ¶éÒ P ÍÂÙè¹Í¡ÊÒÁàËÅÕèÂÁ àÃÒ¨Ðä´éÇèÒ ÊÒÁàËÅÕèÂÁ´éÒ¹à·èÒÃÙ»¹ÕéÁÕ¤ÇÒÁÂÒÇ´éÒ¹ÅÐ 3 ˹èÇÂ
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#7
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á¤èÃÙéÇèÒãªéÊٵà heron ÀÒ¾¢Öé¹ÁÒàŤÃѺ ¤ÓµÍºÍÍ¡Áҷѹ·ÕàÅ ¢Íº¤Ø³ÁÒ¡¤ÃѺ ¼Á¤Ô´äÁèÍÍ¡¨ÃÔ§æ ¼Áâ§èÁÒ¡
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#8
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⨷Âì¢é͹Õé ¶éÒà»ÅÕè¹⨷ÂìãËÁèà»ç¹´Ñ§¹Õé
¡Ó˹´ P à»ç¹¨Ø´·ÕèÍÂÙèÀÒÂã¹ÊÒÁàËÅÕèÂÁã´æ ABC ¶éÒ¤ÇÒÁÂÒǢͧ´éÒ¹ PA, PB áÅÐ PC à·èҡѺ 5, 7 áÅÐ 8 ˹èÇ µÒÁÅӴѺ áÅéÇ ¤ÇÒÁÂÒǢͧ´éÒ¹ AB à·èҡѺà·èÒã´ ¾ÍÁÕÇÔ¸Õ·ÓäËÁ¤ÃѺ
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ÁÒËÒ¤ÇÒÁÃÙéäÇéµÔÇËÅÒ¹ áµèËÅÒ¹äÁèàÍÒàÅ¢áÅéÇ à¢éÒÁÒ·ÓàÅ¢àÍÒÁѹÍÂèÒ§à´ÕÂÇ ¤ÇÒÁÃÙéà»ç¹ÊÔè§à´ÕÂÇ·ÕèÂÔè§ãËé ÂÔè§ÁÕÁÒ¡ ÃÙéÍÐäÃäÁèÊÙé ÃÙé¨Ñ¡¾Í (¡àÇ鹤ÇÒÁÃÙé äÁèµéͧ¾Í¡çä´é ËÒäÇéÁÒ¡æáËÅдÕ) (áµè¡çÍÂèÒãËéÁÒ¡¨¹·èÇÁËÑÇ àÍÒµÑÇäÁèÃÍ´) |
#9
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ÍéÒ§ÍÔ§:
ÊÁ¡Ò÷Õè 1 : ¤Ô´¨Ò¡Êٵà Heron (µÔ´µÑÇá»Ã a,b,c) ÊÁ¡Ò÷Õè 2 : ¤Ô´¨Ò¡Êٵà Cosin (Low of Cosine) ãªéÁØÁ A (µÔ´µÑÇá»Ã a,b,c,A) ÊÁ¡Ò÷Õè 3 : ¤Ô´¨Ò¡Êٵà Cosin (Low of Cosine) ãªéÁØÁ B (µÔ´µÑÇá»Ã a,b,c,B) ÊÁ¡Ò÷Õè 4 : ¤Ô´¨Ò¡Êٵà Cosin (Low of Cosine) ãªéÁØÁ C = 180-(A+B) (µÔ´µÑÇá»Ã a,b,c,A,B) ÊÁ¡Ò÷Õè 5 : ¤Ô´¨Ò¡ÊÙµÃÁØÁ·Õè¨Ø´ P ÃÇÁ¡Ñ¹à»ç¹ 180 ͧÈÒ â´ÂãªéÊٵà Cosin ªèǤӹdz´éÇ (µÔ´µÑÇá»Ã a,b,c) ¤Ô´ÇèÒ¤§·ÓµèÍä´éáÅéǹФÃѺ .... |
#10
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¢Íº¤Ø³¤Ø³¤Ø³ªÒ¹éͤÃѺ
áÅéÇÁÕÇÔ¸ÕÍ×蹺éÒ§äËÁ¤ÃѺ àªè¹áººÇèÒ ËÁعÊÒÁàËÅÕèÂÁàÅç¡¢éҧ㹠ä»á»ÐÍÕ¡´éÒ¹à»ç¹ÊÒÁàËÅÕèÂÁ´éÒ¹¹Í¡·ÕèµÔ´¡ÑºÊÒÁàËÅÕèÂÁ ABC ·Ó¹Í§¹Õé
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ÁÒËÒ¤ÇÒÁÃÙéäÇéµÔÇËÅÒ¹ áµèËÅÒ¹äÁèàÍÒàÅ¢áÅéÇ à¢éÒÁÒ·ÓàÅ¢àÍÒÁѹÍÂèÒ§à´ÕÂÇ ¤ÇÒÁÃÙéà»ç¹ÊÔè§à´ÕÂÇ·ÕèÂÔè§ãËé ÂÔè§ÁÕÁÒ¡ ÃÙéÍÐäÃäÁèÊÙé ÃÙé¨Ñ¡¾Í (¡àÇ鹤ÇÒÁÃÙé äÁèµéͧ¾Í¡çä´é ËÒäÇéÁÒ¡æáËÅдÕ) (áµè¡çÍÂèÒãËéÁÒ¡¨¹·èÇÁËÑÇ àÍÒµÑÇäÁèÃÍ´) |
#11
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ÍéÒ§ÍÔ§:
àÃÒÊÒÁÒöà¢Õ¹ $a,b,c$ ãËéÍÂÙèã¹ÃÙ»ÁØÁ·Õèà¡Ô´¨Ò¡ $PA,PB,PC$ ä´éâ´Âãªé¡®¢Í§ cosine ¤ÃѺ
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site:mathcenter.net ¤Ó¤é¹ |
#12
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ÁÒ¤Ô´´ÙÍÕ¡·Õ ¶éÒ¡Ó˹´¢éÍÁÙÅá¤è¹Õé
àÃÒÊÒÁÒöÊÃéÒ§ÁØÁµèÒ§æ¨Ò¡¨Ø´ P â´ÂãËé PA, PB áÅÐ PC à·èҡѺ 5, 7 áÅÐ 8 ˹èÇ µÒÁÅӴѺ ä´éËÅÒ¡ËÅÒ ¡ç¨Ðà¡Ô´ÊÒÁàËÅÕèÂÁ ABC ·ÕèËÅÒ¡ËÅÒ ´Ñ§¹Ñé¹´éÒ¹ AB ¡çÁÕËÅÒ¡ËÅÒ¤ӵͺ ´Ñ§¹Ñé¹ ¢éÍÁÙÅ⨷Âì·Õè¼Áà»ÅÕè¹ ¨Ö§äÁè¹èҨФú¶éǹÊÁºÙÃ³ì ¶Ù¡äËÁ¤ÃѺ
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ÁÒËÒ¤ÇÒÁÃÙéäÇéµÔÇËÅÒ¹ áµèËÅÒ¹äÁèàÍÒàÅ¢áÅéÇ à¢éÒÁÒ·ÓàÅ¢àÍÒÁѹÍÂèÒ§à´ÕÂÇ ¤ÇÒÁÃÙéà»ç¹ÊÔè§à´ÕÂÇ·ÕèÂÔè§ãËé ÂÔè§ÁÕÁÒ¡ ÃÙéÍÐäÃäÁèÊÙé ÃÙé¨Ñ¡¾Í (¡àÇ鹤ÇÒÁÃÙé äÁèµéͧ¾Í¡çä´é ËÒäÇéÁÒ¡æáËÅдÕ) (áµè¡çÍÂèÒãËéÁÒ¡¨¹·èÇÁËÑÇ àÍÒµÑÇäÁèÃÍ´) |
#13
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¶éÒ¡Ó˹´à»ç¹ÊÒÁàËÅÕèÂÁã´æ ¢é͹Õé¨Ðá¡é§èÒÂÁÒ¡¤ÃѺ á¡éâ´Âãªé ÁѸ°ҹ¢Í§ÊÒÁàËÅÕèÂÁ¤ÃѺ
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#14
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¤ÃٹзÓÍÂèÒ§ääÃѺ ªèÇÂà©ÅÂãËé˹èͤÃѺ
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ÁÒËÒ¤ÇÒÁÃÙéäÇéµÔÇËÅÒ¹ áµèËÅÒ¹äÁèàÍÒàÅ¢áÅéÇ à¢éÒÁÒ·ÓàÅ¢àÍÒÁѹÍÂèÒ§à´ÕÂÇ ¤ÇÒÁÃÙéà»ç¹ÊÔè§à´ÕÂÇ·ÕèÂÔè§ãËé ÂÔè§ÁÕÁÒ¡ ÃÙéÍÐäÃäÁèÊÙé ÃÙé¨Ñ¡¾Í (¡àÇ鹤ÇÒÁÃÙé äÁèµéͧ¾Í¡çä´é ËÒäÇéÁÒ¡æáËÅдÕ) (áµè¡çÍÂèÒãËéÁÒ¡¨¹·èÇÁËÑÇ àÍÒµÑÇäÁèÃÍ´) |
#15
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µèÍ PA ä»áºè§¤ÃÖè§ BC ·Õè¨Ø´ E
PA ÁÕ¤ÇÒÁÂÒÇ 2 ã¹ 3 = 5 ´Ñ§¹Ñé¹ PE = 2.5 ·Ó¹Í§à´ÕÂǡѹ µèÍ PB ä»áºè§¤ÃÖè§ AC ·Õè¨Ø´ F ¨Ðä´é PF = 3.5 áÅÐ µèÍ Pc ä»áºè§¤ÃÖè§ AB ·Õè¨Ø´ D ¨Ðä´é PD = 4 ËÅѧ¨Ò¡¹Õé¡çá¡éäÁèÂÒ¡áÅéǤÃѺ |
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