CHỨNG MINH: \(m^4-2m^3+2m^2-2m+1\ge0\) với mọi m
2/GIAI PHUONG TRINH:
a) \(x^3-2x-4=0\)
b)\(x^3-7x-6=0\)
3/CHO a+b=5; ab=6. TINH GIA TRI \(a^5+b^5\)
4/Cho hinh thang KLMN (KN//LM) , 2 duong cheo cat nhau tai E . Qua E ke duong thang song song vs KN cat MN tai F. Chung minh \(\frac{1}{EF}=\frac{1}{KN}+\frac{1}{LM}.\)
cho hình thang KLMN (KN//LM) đường chéo cắt nhau tại E . Qua E kẻ đường thẳng song song vs KN cắt MN tại E. Chứng minh \(\frac{1}{EF}=\frac{1}{KN}+\frac{1}{LM}.\)
Cho ( O;R ).Moi duong thang d khong di qua O va cat duong tron tai 2 diem phan bat A va B . Tren d lay M sao cho A nam giua M va B . Tu M ke tiep tuyen MC va MD voi duong tron ( C,D la cac tiep diem ).
1/ Chung minh rang MCOD la tu giac noi tiep .
2/ Goi I la trung diem cua AB . Duong thang IO cat tia MD tai K . Chung minh KD*KM = KO*KI
3/ Moi duong thang ddi qua O va song song voi CD cat cac tia MC va MD lan luot tai E va F . X ac dingh vi tri cua M tren d cho dien tich tam giac MEF dat gia tri nho nhat
Giai giup minh cau c, va cau d, minh dang can gap...
từ 1 điểm A nam ngoai (O) ke 2 tiep tuyen AB va AC den (O) (B,C la tiep diem) . cat tuyen ADE khong di qua tam O ( D nam giua A va E), goi I la trung diem cua DE
a, chung minh 5 diem A, B, O, I , C cung nam tren 1 duong tron suy ra IA la tia phan giac goc BIC.
b, BC cat AE tai K chung minh KA.KI =KD.KE
c, qua C ke duong thang song song AB duong thang nay cat cac duong BE, BD lan luot tai P, Q . chung minh C la trung diem cua PQ.
d, duong thang OI cat (O) tai S va H. HK cat (O) tai T chung minh A, T, S thang hang
Cho (O) duong kinh AB. Ve duong thang d vuong goc voi AB tai B, ve duong kinh MN bat ky khong trung voi AB. Cac tia AM va AN cat d theo thu tu tai cac diem E va F
1, Tu giac AMBN la hinh gi?
2, Chung minh Tu giac MNFE noi tiep
3, Chung minh AM . EF = AF.MN
4, Chung minh: Khi duong kinh MN quay quanh O nhung khong trung voi AB thi tam duong tron di qua 4 diem M,N,F,E luon nam tren 1 duong thang co dinh
Cho (O) duong kinh AB. Ve duong thang d vuong goc voi AB tai B, ve duong kinh MN bat ky khong trung voi AB. Cac tia AM va AN cat d theo thu tu tai cac diem E va F
1, Tu giac AMBN la hinh gi?
2, Chung minh Tu giac MNFE noi tiep
3, Chung minh AM . EF = AF.MN
4, Chung minh: Khi duong kinh MN quay quanh O nhung khong trung voi AB thi tam duong tron di qua 4 diem M,N,F,E luon nam tren 1 duong thang co dinh
giup mk cau 4 n:)))
giai giup cau c va d may ban
Cho tam giac ABC (AB < AC) co 3 goc nhon. (O) duong kinh BC cat 2 canh AB,AC lan luot tai E,F. D la giao diem cua AH voi BC.
b, chung minh EC la tia phan giac goc DEF
c,EF cat BC tai M. chung minh ME.MF=MD.MO=MB.MC
d, duong thang qua D va song song MF , cat AB va AC lan luot tai K va L . chung minh M,K.O.L cung thuoc 1 duong tron.
cho tam giac ABC vuong tai A (AB>AC). tren AC lay M khac A va C. Duong tron duong kinh MC cat BC tai E va cat duong thang BM tai D( E khac C va D khac M).
a) chung minh tu giac ABCD noi tiep.
b) chung minh goc ABD= goc MED
c) duong thang AD cat duong tron duong kinh MC tai N( N khac D) duong thang MD cat CN tai K , MN cat CH tai H, chung minh KH song song NE
Giai giup minh cau d, cua bai nay nha
1.Cho (O;R) co duong kinh BC, tren doan thang OB lay H sao cho OH<HB. Ve day AF cua (O) vuong goc voi BC tai H
a, chung minh tam giac ABC vuong tai A va HB.HC=HA.HF
b, Tren AH lay D sao cho AD<DH. Tia BD cat (O) tai E. chung minh AB2=BD.BE
c, tiep tuyen tai B cua (O) cat tia CA tai M. Goi N la hinh chieu cua O tren AB. chung minh goc BMN=goc OMC.
d, qua F ve duong thang song song BC cat tia AB tai P. Goi K la trung diem cua HC. chung minh PH vuong goc AK.
cho duong tron tam O duong kinh AB .Ve hai day AM va BN song song voi nhau sao cho so do BM nho hon 90 do .Ve day MD song song voi AB.Day DN cat AB tai E. Tu E ve 1 duong thang song song voi AM cat duong thang DM tai C. Chung minh
a)AB vuong goc DN
b)BC la tiep tuyen cua duong tron (O)
