2 thoughts on “Hình học 2007”

  1. Bai 1.( China Northern MO 2007)
    Cho tam giac nhon ABC. Duong tron voi duong kinh AB cat CA,CB tai M,N tuong ung. Ve CT\perp AB va cat duong tron tren tai T, o do C,T nam cung phia doi voi duong thang AB.S la diem tren AN sao cho BT=BS. Chung minh rang BS\perp SC.

    Bai 2.( China Northern MO 2007)
    Ban kinh duong tron noi tiep cua tam giac ABC bang 1 va cac canh cua no la cac so nguyen. Chung minh rang no la tam giac vuong.

    Bai 3.(Bulgaria TST 2007)
    Cho tam giac ABC voi \angle BAC=\dfrac{\pi}{6} va ban kinh duong tron ngoai tiep bang 1. Neu X la diem nam trong hoac tren bien cua tam giac thi ta dat m(X)=\min (XA,XB,XC). Tim tat ca cac goc cua tam giac nay neu \max (m(X))=\dfrac{\sqrt{3}}{3}.

    Bai 4.(Bulgaria TST 2007)
    Trong tam giac can ABC(AC=BC) diem M nam trong doan AB sao cho AM=2MB,F la trung diem cua BC va H la hinh chieu vuong goc cua M tren AF. Chung minh rang \angle BHF=\angle ABC.

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