%GỌI% C (T;−2T−5).%GỌI%I%LÀ%TÂM%HÌNH%CHỮ%NHẬT%ABCD,%SUY%RA%I%LÀ%TRU...

2.%Gọi% C (t;−2t−5).%Gọi%I%là%tâm%hình%chữ%nhật%ABCD,%suy%ra%I%là%trung%điểm%của%AC%và%BD.%⎞⎛Do%đó%I t−4⎜⎜⎟.%Tam%giác%BDN%vuông%tại%N%có%I%là%trung%2 ;−2t+32⎠⎟⎟⎟⎝⎜⎜%điểm%BD%nên%IN=BD2 =IB=IA.%

2

83Ta%có%pt:%+ −1+ 8−−2t+3= −4−t−4⇔t=1.%⎟13−t−413−−2t+3 Suy%ra%I −3⎟;C (1;−7).%2;1Gọi%B(a;b)%ta%có% CM! "!!=2BC! "!!=2(1−a;−7−b)⇒M (3−2a;−21−2b).%Ta%có%BN! "!!= 83−13a= 44+26a⎟,MN! "!!!⎟.%13 ;272+26b1313 ;−1+13bDo%BN%vuông%góc%với%MN%nên:%.MN! "!!!=0⇔(83−13a)(44+26a)−(1+13b)(272+26b)=0 (1).% BN! "!!Mặt%khác:%IB

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=IC

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=125+ b−1=1252 (2).%%%%%%%%2 ⇔ a+3Từ%(1)%và%(2)%ta%có:%⎡a= −4,b= −7⎧⎨⎢⎢⎪⎪% a

²

+b

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+3a−b=60.%⇔ 2a−3b=13a=8313(a

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+b

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)−61a+137b−130=0a

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+b

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+3a−b=60⎩⎪⎪ ⇔⎩⎪⎪