Dựng đường cao BH.
Xét tam giác vuông CHB ta có .\(BC^2=BH^2+HC^2=BH^2+\left(AC-AH\right)^2\)
\(=BH^2+AH^2+AC^2-2AC.AH\)
Ta có \(AH=CB.\cos A\)
suy ra \(BC^2=BH^2+AH^2+AC^2-2AC.CB.\cos A\)
Hay \(BC^2=BA^2+AC^2-2AC.BC.\cos A\)
\(\Leftrightarrow a^2=b^2+c^2-2bc\cos A\)
cho tam giac abc ,có A=90 ,AB =c,AC=b,BC=A.cmr a2=b2+c2+bc
cho tam giac abc can tai a. canh ab,bc,ac tiep xuc voi duong tron tam o tai cac dem d,e,f. bf cat (o) tai i, di cat bc tai m. chung minh:
a)tam giac def co 3 goc nhon
b)df // bc
c)tu giac bdfc noi tiep
d)bd/cb =bm/cf
1/cho tam giac ABC can tai A ( goc A<900) cac duong cao AD va BE cat nhau tai H ( D thuoc BC, E thuoc AC)
a/CM tu giac DHEC noi tiep duong tron
b/chung minh ED=BD va goc HBD=goc HCD
c/Goi O la tam cua duong tron ngoai tiep tam giac AHE.CM rang ED la tiep tuyen cua duong tron (O)
2/cho ram giac ABC co ba goc nhon noi tiep duong tron (O).Hai duong cao AD va BJ cat nhau tai H
a/CM;tu giac CDHK noi tiep
b/ve d.kinh AF .tia AD cat (O)tai E.CM BC//EF
c/CMR; AD/HD=BD.CD
b/goi I la trung diem cua BC .CMR: H,I,F thang hang
3/cho tam giac nhon ABC noi tiep duong tron tam O,duong cao BHva CK lan luot cat duong tron tai Eva F
a.CMR: tu giac BKHC noi tiep
b.CM: A la diem chinh giua cu cung EF
c.CM:OA//EF
d.CM:EF//HK
4/cho tam giac ABC vuong tai A co AB<AC.Ke duong cao AH.Tren HC lay diem D sao cho HD=Hb
a/CMR:tap giac ABD can
b/Tu C ke CF vuong goc voi AD keo dai tai E
Chung minh tu giac AHEC noi tiep duoc trong 1 duong tron .Xac dinh tam O cua duong tron nay
c/CM:AB.ED=HB.CD
cho tam giác abc co 3 goc nhon .Đương (O) đương kinh BC căt AB,AC tai E va D,BD căt CE tai H,AH cát BC tai I
a,c/m tư giac ADHE,ADIB nôi tiêp
b c/m AD.AC=AH.AI=AE.AB
c,Ve 2 tiêp tuyên AMva AN cua (O) .c/m M,H,N thang hang
giúp min câu B,C vs a
cho tam giac ABC vuong tai A co BC=a AC=b AB=c
tim GTNN cua M = 8a^2(1/b^2 +1/c^2) + (b+c)/a +2016
Cho tam giac ABC co canh AB=24cm,AC=18cm,BC=30cm.Ke duong cao AK.Ke KP\(\perp\)AC. a,Chung minh tam giac ABC la tam giac vuong. b,Tinh do dai AK,BK. c,Chung minh AP.AC=AB2-KB2. d,Chung minh AP.AC=KB.KC=PK.AB.
cho tam giac ABC nhon ,duong phan giac AD.biet AB=c;AC=b.tinh AD theo b,c
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
Bai 1 giai tam giac ABC vuong tai A, biet
a/ AB = 6cm, ˆBB^ = 40
b/ AB= 10cm, ˆCC^ = 35
c/BC=32cm, AC = 20cm
d/ AB = 18cm, AC=21cm
Bai 2 Cho △ABC co AB=40cm , AC=58cm , BC=42cm
a/ △ ABC co phai la tam giac vuong hay k ? vi sao ?
b/ Ke duong cao BH cua tam giac . Tinh do dai BH ?
c/ Tinh ti so luong giac cua goc A
Bai 3 : Cho △ABC co AB=5cm , ˆBB^ =60 , ˆAA^ = 45
a/ tinh do dai BC va AC
b/ Tinh dien tich △ABC