Page 2 - 微言“瓜豆原理”++浅谈“解题模型”
P. 2
ᇏ࿐ඔ࿐ᄖᆽ 2019 ୍ֻ 8 ௹ ZHONGXUESHUXUEZAZHI
a － b 1 1
． ٳљ࠹ෘ S △ABL = ·AB·LKđS △ACL = ·AC
1 2 2
2sin α
2 ·LMđ෮ ၛ S + S =
△ABL △ACL
4 ႋႨ 1 1
̵ AB + AC̶ ·AL·sin A．
4．1 ᆰࢤႋႨࢲં 2 2
̵ 2019 ୍ᇛը၂ଆ̶ ೂ 1
S AKNM = · AN ·
7đ ඹшྙ ABCD ଽࢤႿჵ Ođ 2
AB = 9đAD = 15đ ∠BCD = 1
̵ AK + AM̶ ·sin A．
120°đ ༿ AC ٳ ∠BADđ ࢘ 2 8
ٳཌ AC ֥Ӊ． ᆺླေဒᆣ̵ AB + AC̶ ·
ٳ༅ ABCD ൞ჵଽࢤ AL = ̵ AK + AM̶ ·AN ࠧॖ．
ඹшྙđ མ֞ჵᇛ࢘ ∠BAD = 7 ۴ऌభ໓ྻඍđAB + AC = 2ADđAK + AM = 2AK．
60°đ ༿ AC ൞ჵᇛ֥࢘࢘ٳཌđ ০Ⴈభ໓ิ֥ࠣჵ AK
֩ൔሇ߄ູ AD·AL = AK·ANđ ္ࣼ൞ေᆣૼ =
ᇛ࢘࢘ٳཌӉ؇֥࠹ෘ܄ൔđ սೆඔऌࠧॖ֤ AD
ࢲݔđ ݖӱ． AL ．Ⴎ KL ∥ DNđ ಸၞ֤ԛ AK = AL Ӯ৫．
AN AD AN
4．2 ႋႨࢳีනਫ਼
ҕॉ໓ང
̵ ֻ 28 ࢽ IMO ֻ 2 ี̶ ೌ࢘࢘ྙ ABC ֥פ࢘
ŀ1ł ້བ．၂োᆰࣥࢌ༿෮Ӯඹ่ཌ؍Ӊ؇໙ี֥၂Ϯࢲ
A ֥ଽٳ࢘ཌࢌ BC шႿ Lđ Ⴛࢌ࢘ྙ֥ຓࢤჵႿ
ં ŀJł．ᇏ࿐ඔ࿐ᄖᆽđ2019̵ 2̶ ͇ 43－44．
Nđ ݖ L ٳљቔ AB ބ AC ш֥Լཌ LK ބ LMđ Լቀ൞
ŀ2ł ቐིđ ա༌ת．၂֡ᇏॉี֥ࢳճ、 ຉᅚ、 აэൔŀJł．ᇏ
K ބ M．ᆣ͇ ඹшྙ AKNM ֥૫ࠒ֩Ⴟ࢘ྙ ABC
࿐ඔ࿐ᄖᆽđ2019̵ 2̶ ͇ 58－60．
֥૫ࠒ．
ٳ༅ ༵ቔԛ໙ี֥ྙđ ೂ 8đ ေᆣૼ ቔᆀࡥࢺ ม̵ 1979—̶ đ ଳđ תۚౝದđ ᇏ࿐၂ࠩ࢝
đ
S = S AKNM ॖၛሇ߄ູ S + S = S + ഽđ ᇶေՖ൙Ԛᇏඔ࿐࢝࿐۽ቔđ ᄻࠆۚౝཅज़၂֩ࢂđ ۚ
△ABC △ABL △ACL △AKN
S ． ౝཅ࢝ഽࠎЧۿն၂֩ࢂ．
△AMN
ັ “ܨჰ” రซ “ࢳีଆ”
ᆄࡾസୡѯўݚݓ࠽ކቔ࿐ 315800 ਾౢಅ
ׄ໙ีܼٗթᄝႿ൦૫ބቕѓ૫ଽđ ა ၂่ᅼཌ؍đ ܥקఃᅼ͈ׄ ਣшקб২đ ࡃ࢘҂ڿэ．ᇶ
ఃཌྷܱ֥ᄎਫ਼ӱࢳࠣཌ؍ቋᆴಒק֥໙ีൈ༯ Ⴟᆰཌđ ՖႿᆰཌ͈ ᇶႿ̵ ̶ ჵđ ՖႿ̵ ̶
նಣđ ཌྷܱ֥ᇏॉᆇี̵ ᇏॉଆ۷؟̶ ҂഻ई．ᄝ ჵ．ऎุॖྙӮೂ༯֥ਆ۱ଁี͇
ᇙ؟֥ࢳҦᇏ đ“ ܨჰ” ႮႿ૰೪၂ᇙᇠี ଁี 1 ೂ 1đ AđBđC ູ૫ଽ֥۱ׄđ ׄ
طնྛః֡．ཌྷܱ֥໓ᅣđ ၂ൈࡗᄝ௹़ᄖᆽ、 ህြ A ູקׄđ ׄ B ᄝקᆰཌ l ഈᄎđ ᄝᄎݖӱᇏđ Ќӻ
ࠡބ৳ຩഈಣၰ．гᆀᇿၩ֞đ धնඔ֥໓ᅣđ ࠇ ∠BAC = α̵ 0° ＜ α ＜ 180°̶ đ AC = k·AB̵ k ＞ 0̶ ҂
ห൹֞၂Ϯֹ݂ବđ ࠇ၂Ϯ֞ห൹ֹဆၶđ бࢠࠢᇏ э．ᄵׄ C ္ᄝଖ၂קᆰཌഈᄎ．
ᄝุဒࢳم֥ބཾྟഈđ ္ࣼ൞ᄝ “ ܨჰ” ֥ຓ
ഈቔ໓ᅣđ ໃԨஷఃଽݤđ หљ൞۲ᇕᄝཌ࢝ტ֥൪
ᇏđ ҂ః෮ၛಖ．
ᆩః෮ၛಖđ ֤۷ۚჹđ ؓႿඔ࿐໙ีđ ॖၛն։
ࡌഡđ ླࣈരᆣ．Ⴕсေؓ “ ܨჰ” ࣉྛ௩༅．
1 ྙӮଁี 1 2
હ൞ “ ܨჰ” ͌ ఃࠎЧေၬгᆀۀওູ͇
ଁี 2 ೂ 2đ AđBđC ູ૫ଽ֥۱ׄđ ׄ
4 1
