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Cho tu giac ABCD co goc A=C=90° .Chung minh. a) 4diem A, B, C, D cung thuoc mot duong tron
b) so sang BD va AC
bai 1:Cho duong tron tam O, day AB. cac tiep tuyen ke tu A,B cat nhau tai C. ke day CD cua duong tron co duong kinh OC(D khac A,B). CD cat cung nho AB cua (O) tai E (E nam giua C va D).Chung minh:
a/goc BED= goc DAE
b/DE^2=DA*BD
bai 2:Cho tam giac ABC deu noi tiep duong tron tam O. M la diem nam tren cung nho AB. chung minh:
a/MB+MA=MA
b/ke MH vuong goc voi BC, MI vuong goc voi AB, MK vuong goc voi AC. chung minh 3 diem H,I,K thang hang
cho tam giac ABC vuong tai B .AB=3cm ;AC=4,5cm.Ve phan giac AD (D thuoc BC).Tu D ve DE vuong goc voi AC (E thuoc AC).Goi K la giao diem cua ED va AB
1:Chung minh rang BD=ED
2:Chung minh rang tam giac AKC can
3:Tren tia doi tia KE lay diem F sao cho KF=BC.Chung minh rang EB di qua trung diem cua AF
Cho 2 hinh chu nhat co cung dien tich .HInh 1 co kich thuoc a va b (a lon hon b) hinh 2 co kich thuoc c va d (c lon hon d) .chung minh rang nêu a lon hon c thi chu vi cua hinh1 lon hon chu vi hinh 2
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
voi a,b,c,d, la cac so duong thoa man a*b = c*d =1 chung minh bat dang thuc : ( a+b )*( c+d ) +4 >= 2*( a+b+c+d ) cac ban oi giup minh voi OK
Cho tam giac ABC vuong tai A, AH la duong cao, AM la duong trung tuyen. Goi D va E theo thu tu la cha duong vuong goc ha tu H den AB va AC
a) chung minh AM vuong goc voi DE
b) Cho AH =2cm, BC = 5cm. Tinh dien tich tu giac ADHE
c) Chung minh rang: \(\sqrt{HB>HC}\)=\(\sqrt[3]{B\text{D}.CE.BC}\)
giai ho minh bai nay voi
cho a,b,c la do dai 3 canh tam giac va an;bn;cn cung la do dai 3 canh tam giac voi n la so nguyen duong. Chung minh rang 2 trong 3 so a,b,c bang nhau
Voi a,b,c la cac so duong thoa man a*b =c*d =1 chung minh (a+b)(c+d) + 4>= 2(a+b+c+d)
