1. cho tam giac ABC M;N lan luot la trung diem cua CA ,CB ;I la diem bat ki tren MN (I khac M;N ) C/M trong 3 tam giac ICB;ICA;IAB; co 1 tam giac ma dien tich cua no bang tong cac dien tich cua 2 tam giac con lai
2. cho tam giac ABC tren cac canh AB;AC;CA keo dai ve phia B;C;A lay B1;C1;A1 sao cho BB1=b;CC1=c; AA1=a c/m a/AC+b/ AB+c/BC>HOAC =3
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
Tam giác ABC, lấy C1 thuộc AB, A1 thuộc BC, B1 thuộc AC biết AA1, BB1, CC1 bé hơn hoặc bằng 1. CMR SABC bé hơn hoặc bằng 1/căn 3
cho tam giac nhon ABC, cac duong cao AA1, BB1, CC1 cat nhau tai H
a) chung minh neu SHAB = dien tich HBC = dien tich HAC thi ABC deu
b CM AH/A1h+ BH/B1H + CH/C1H > 6
Bai 1
Cho tam giac ABC co AB=AC.Lay diem h thuoc AC.Diem k thuoc AB sao cho AH=Ak.Goi O la giao diem cua BH va CK.Chung Minh
a,Tam giac OKB=tam giacOHC
b,AO la phan giac cua goc BAC
Cho nua duong tron (o) duong kinh AB va C la diem chinhgiua cung AB. Lay M thuoc cung BC va N thuoc tia Am sao cho AN=Bm.Ke day CD//AM
A chung minh tam giac ACN=tam giac BCM b. Chung minh tam giac CNM la tam giac vuong can
c. tu giac ANCD la hinh gi?vi saop?
Cho tam giac ABC vuong tai A, duong cao AH ( H thuoc BC) va phan giac BE cua ABC ( E thuoc AC), AH va BE cat nhau tai I. CM:
a) IH.AB = IA.BH
b) Tam giac BHA dong dang voi tam giac BAC va AB2 = BH.BC
c) IH/IA = AE/EC
1/ cho tam giac ABCco 3 goc nhon noi tiep duong tron (O).Hai duong cao AD va BKcat nhau tai H
a/CM tu giac CDHK noi tiep duong tron
b/Ve duong kinh AF tia AD cat (O)tai E.CM BC//EF
c/CMR.AD.HD=BD.CD
2/ cho hinh binh hanh ABCD co dinh D thuoc duong tron duong kinh AB Tu B ha BN vuong goc voi AC ; tu D ha DM vuong goc voi AC.Chung minh
a/.tu giac CBMD noi tiep duong tron
b/tan giac ACD dong dang tam giac BDN
c/DB.DC=DN.AC
3/cho tam giac ABC can tai A (A<900) cac duong cao AD va BE cat nhau tai H ( D thuoc BC, E thuoc AC )Cm ;Tu giac DHEC noi tiep duong tron CM;ED=BDva goc HBD = goc HCDgoi O la tam cua duong tron ngoai tiep tam giac AHE.Chung minh rang ED la tiep tuyen cua duong tron (O)cho tam giac nhon abc nt duong tron tam (O;R) H la truc tam I,K lan luot la chan duong cao ke tu dinh A,B cua tam giac ABC(I thuoc BC,K thuoc AC). Goi M la trung diem cua BC Ke HJ Vuong goc voi AM (J thuoc AM)
CM AJK va ACM dong dang