Page 2 - 微言“瓜豆原理”++浅谈“解题模型”
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ZHONGXUESHUXUEZAZHI                                      ᇏ࿐ඔ࿐ᄖᆽ         2019 ୍ֻ 8 ௹


            A ູקׄđ ׄ B ᄝ϶ູࣥ r ֥ק ⊙O ഈᄎ׮đ ᄝᄎ׮ݖ                  ๎֥ԩ৘Ϸم．
            ӱᇏđ Ќӻ ∠BAC = α̵ 0° ＜ α ＜ 180°̶ đ ౏ AC = k·            2．ၛ “ ҂эਈ ”“ ໊ර࿈ሇ” ్ູೆׄ．
            AB̵ k ＞ 0̶ ҂э．ᄵׄ C ္ᄝ၂קჵഈᄎ׮．                           ̵ 1̶ ଁี 1 ֥ᆣૼ͇
            2   ᆣૼଁี                                               ೂ๭ 5đ ቔ AB ⊥ lđ ቔ
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                гᆀՖೂ༯֥ਆ۱๯ࣥೆ൭࿙౰ࢳճҦ੻͇                            AC đ ൐֤ ∠B AC = αđAC =
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                1．ࠎႿ “ ໊ර࿈ሇ”đ ၛ “ਆׄקཌ ”、“೘ׄקჵ”                 k·AB đ ᆰཌ CC ࢌᆰཌ l Ⴟ
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            ູ๬௥ׄ．                                              ׄ Pđ ၞ ᆣđ △ACC      0  ∽
                ̵ 1̶ ଁี 1 ֥ᆣૼ͇                                 △ABB đ Ֆ طđ ∠AC C =
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                                                                                                 ๭ 5
                ೂ๭ 3đ ֒ׄ B ᄎ׮֞                                 ∠AB B = 90°đ ࣉطđ β = α．
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            B'đ ׄ C ෛᆭᄎ׮֞ C' ൈđ ৵                                  ཬࢲ    ൙ൌഈđ ࢳथ׮ׄ໙ี֥၂۱ܱ࡯ׄ൞࿙
            ࢤ BC、B'C' ࢌႿׄ Dđ ৵ࢤ                                ᅳ “ ҂эਈ”đ קׄ A ֞קᆰཌ l ֥ए৖———“ׄཌए
            ADđ ᆰཌ CC' ࢌᆰཌ l Ⴟׄ P．                             ৖” ൞၂۱҂эਈđ ቔ్ູೆׄđ ڣၛ “໊ර࿈ሇэ
                ၹ ູ ∠B'AC' = α =                               ߐ”đ ၛ “ קׄ·ק࢘” ູઋ࢖ׄᆣૼՖ׮ׄᄝ၂קᆰ
                   AC'       AC               ๭ 3              ཌഈᄎ׮．
            ∠BACđ      = k =    đ ෮ၛ
                   AB'       AB                                    ᆃဢ֥ࢳ൤҂ࣇࡥჿၞ׭đ ط౏္ಒקਔՖ׮ׄ
            △AB'C' ∽ △ABCđ ෮ၛ ∠AB'C' = ∠ABCđ ౏ ∠AC'B'          ֥݅ࠖ ——— ݖקׄ P̵ ᆣૼݖӱᇏၘടࠣఃೂޅಒ
            = ∠ACBđ ෮ၛ AđBđB'đD ඹׄ܋ჵđ ౏ AđDđCđC' ඹׄ            ק̶ ౏აקᆰཌ l ֥ࡃູ࢘קᆴ α．
            ܋ჵđ ෮ၛ ∠AB'B = ∠ADB = ∠AC'Cđ ෮ၛ AđB'đPđ                ̵ 2̶ ଁี 2 ֥ᆣૼ͇
            C' ඹׄ܋ჵđ ෮ၛ β = α．ࠧ೏ׄ BđC Ф౼קđ ᄵ CC' ა                 ᆣૼ͇ ೂ๭6đ ৵ࢤ AOđ ቔ
            ᆰཌ l ֥ࡃູ࢘ αđ Ⴎ C' ֥಩ၩྟॖᆩđ ׄ C ᄝ၂קᆰ                 AO'đ ൐֤ ∠OAO' = αđ ౏ AO'
            ཌഈᄎ׮．                                              = k·AOđ ৵ࢤ BOđCO'đ ၞᆣđ
                ཬࢲ     ᄝ “ ཌྷර೘࢘ྙ” ֥ࠎԤഈđ ๙ݖ “ ඹׄ܋                                     CO'
                                                               △ACO' ∽ △ABOđ Ⴟ൞đ
            ჵ”đ ၛ “ קׄ·ק࢘” ູઋ࢖ׄ൐ଁี֤ၛᆣૼ．༯໓                                            BO
            ട֥ࠣ֞ཌྷර೘࢘ྙ֥ᆣૼაЧ২ᇏ֥ᆣૼ๝৘đ ҂                            AC
                                                               =   = kđ ՖطđCO' = k·rđ ࠧ
            ᄜሕඍ．                                                AB                               ๭ 6
                ̵ 2̶ ଁี 2 ֥ᆣૼ͇                                 ׄ C ᄝၛ O' ູჵྏđ ၛ k·r ູ
                ೂ๭ 4đ ֒ׄ B ᄎ׮֞                                 ϶֥ࣥקჵഈᄎ׮．
            B'đB″đ ׄ C ෛᆭᄎ׮֞ C'đC″                                 ཬࢲ    קׄ A ֞קჵ֥ჵྏ O ֥ए৖———“ ׄྏ
            ൈđ ඨՑ৵ࢤ BđB'đB″͈ CđC'đ                             ए৖” ൞၂۱ “ ҂эਈ”đ ၛՎ్ູೆׄđ ڣၛ “໊ර࿈
            C″．ၞᆣ △ABB' ∽ △ACC'đ Ⴟ                             ሇэߐ”đ ၛ “ קׄ·קӉ”ູઋ࢖ׄᆣૼՖ׮ׄᄝ၂

               CC'                                             קჵഈᄎ׮．
            ൞đ     = kđ ᄵ CC' = k·BB'đ
               BB'                                                 หљֹđ ֒ α = 0° ࠇ 180° ൈđ ࢲં္Ӯ৫đ Վൈđ
            ၞᆣđ △ABB″ ∽ △ACC″đ Ⴟ              ๭ 4              ׄ C ᄝཌ؍ AB ࠇః࿼Ӊཌഈđ ೏ k = 1đ ᄵՎൈ֥эߐ
            ൞đ ∠AB″B = ∠AC″Cđ ၞᆣđ                              ູࠧ “ ࿈ሇэߐ”．๝ൈđ ၞᆩՖ׮֥ׄᄎ׮ਫ਼ӱ S' ࠧ
            △AB'B″ ∽ △AC'C″đ Ⴟ ൞đ ∠AB″B' = ∠AC″C'đ             ູᇶ׮֥ׄᄎ׮ਫ਼ӱ S ֥ k Пđ Ⴟ൞౰ࢳՖ׮֥ׄᄎ
            ∠AB″B － ∠AB″B' = ∠AC″C － ∠AC″C'đ ᄵ ∠BB″B' =        ׮ਫ਼ӱൈđ ॉ੮ “ ᇶ׮ׄ”ࡗࢤ౰ࢳສສбॉ੮ “Ֆ׮
            ∠CC″C'đ ࠧ೏ׄ BđB' Ф౼קđ ᄵׄ CđC' ෛᆭФಒקđ
                                                               ׄ” ᆰࢤ౰ࢳ۷ູь০． طຓđ ᇭ؟აՎཌྷܱ֥౰ࢳ
            Ⴛקཌ؍ BB' ֥ᅦ࢘ ∠BB″B' ҂эđ ᄵקཌ؍ CC' ֥                “ ֆ׮ׄ ——— ֆཌ؍” ֥ቋཬᆴ֥໙ีđ ӈӈॖၛ০
            ᅦ࢘ ∠CC″C' ҂эđ ࠧׄ C″ ᄝ၂קჵഈᄎ׮．                       Ⴈ “ ܨ׸ჰ৘” ಒק “ ֆ׮ׄ” ֥݅ࠖđ طު০Ⴈ “ Լཌ
                ཬࢲ     ᄝ “ ໊ර࿈ሇ” ֥ࠎԤഈၛ “ קཌ·ק࢘”
                                                               ؍ቋ؋” ࠇ “ ׄྏए৖ࡨ϶ࣥ” টಒק．
                                               )   )
            ູઋ࢖֤ׄᆣ．ׄ B″ ބ C″ ٳљᄝਜ޶BB'đCC' ഈ֥౦                      ֒ಖđ ࠎႿ “ ໊ර࿈ሇэߐ” ᆣૼਔ “ܨ׸ჰ৘”đ
            ྙđ Վԩ҂ᄜሕඍ．                                         ๝ൈđ ๝ဢ္ॖၛ൐Ⴈ “໊ර࿈ሇэߐ”ࢳճॖၛႨ
                ഈඍ֥ᆣૼٚൔđ ؓႿ“ඹׄ܋ჵ”ބ“೘ׄק                        “ ܨ׸ჰ৘” ࢳճ֥໙ี．ೂݔ৘ࢳਔೂഈ֥ਆ۱ଁี
            ჵ” ေ౰ࢠۚđ ࢝ഽބሧႪളၞႿ৘ࢳ．࡫Ⴟགྷྛ࢝ҋ                         ֥ᆣૼđ ପࣼ҂଴৘ࢳ “ܨ׸ჰ৘”֥൐Ⴈေژކс
            ؓ “ ඹׄ܋ჵ”ടࠣ҂؟౏ေ౰ࢠ֮đ ֒࿙౰۷ູຈ                         ေ֥భิ่ࡱ．
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