Câu hỏi của Nguyễn Thị Thanh Trang

Question

Cho $\Delta ABC$vuông tại A, đường cao AH. Vẽ đường tròn tâm O đường kính AH, đường tròn này cắt AB, AC lần lượt tại D và E. Gọi M, N lần lượt là trung điểm của BH, CH.a. Chứng...

Upin & Ipin · Accepted Answer

Minh goi y thoi nhe muon roi mik chuan bi di ngu bn thong cama) ban dung dinh nghia tiep tuyen la xongb) cm O la truc tam tam giac BAN roi dung yeu to // la okc) mik nghi la : de thay Samn=1/2 Sabc (t/c trung tuyen.....)thi Samn Min <=> Sabc minCau c) mik ko chac lam co cau a,b ban cu lam theo mik kieu gi cung raCo gi de mai mik ngu day mik lam choCâu trả lời: Minh goi y thoi nhe muon roi mik chuan bi di ngu bn thong cama) ban dung dinh nghia tiep tuyen la xongb) cm O la truc tam tam giac BAN roi dung yeu to // la okc) mik nghi la : de thay Samn=1/2 Sabc (t/c trung tuyen.....)thi Samn Min <=> Sabc minCau c) mik ko chac lam co cau a,b ban cu lam theo mik kieu gi cung raCo gi de mai mik ngu day mik lam cho

Upin & Ipin · Answer

a) Xet $\Delta ADE$ co AO=DO=EO=R => DE la duong kinh (O)Ta co MD cat (O) duy nhat tai D=> MD la tiep tuyen (O)=> $MD\perp DE$Tuong tu NE la tiep tuyen (O) =>$NE\perp DE$ Suy ra MD//NE ( Quan he tu vuong goc den song song)b) Noi NO , Goi F la trung diem OHXet $\Delta AHC$ co OH=OA ( gt) , HN=NC (gt)=> ON la duong trung binh => ON//ACma AB $AB\perp AC\left(\Delta ABCvuong\right)$Suy ra $NO\perp AB$Xet tam giac ABN co $AH\perp BN\left(gt\right),NO\perp AB\left(cmt\right)$ => O la truc tam tam giac ABN=> $BO\perp AN$ (1)Xet tam giac giac BHO co M la trung diem BH (gt) , F la trung diem OH ( gt)=> MF la duong trung binh => MF//BO (2)Tu (1) va (20 suy ra $MF\perp AN$ (quan he tu vuong goc den song song)Xet tam giac AMN co $\hept{\begin{cases}AH\perp MN\left(gt\right)\MF\perp AN\left(cmt\right)\end{cases}\Rightarrow}$ Trung diem F cua OH la truc tam $\Delta AMN$c) Xet tam giac ABH co AM la duong trung tuyen =>Samh =Sabm ( t/c trug tuyen chia cat doi dien thang 2 phan co dien h bag nhau)=> Samh=1/2Sabhtuong tu ta cung co Sahn = 1/2 SahcSuy ra Samh+Sahn =1/2 (Sabh +Sahc) <=> Samn=1/2 Sabc=> Samn min <=> Sabc minTheo minh thi tam giac ABC can co dk la dien h tam giac ABC nho nhat thi Samn dat gtnnMik ko chac cau c) lam dau. Neu sai mong cac bn thong cam ma sua ho mik,Mik cam on.Chuc ban hoc totCâu trả lời: a) Xet $\Delta ADE$ co AO=DO=EO=R => DE la duong kinh (O)Ta co MD cat (O) duy nhat tai D=> MD la tiep tuyen (O)=> $MD\perp DE$Tuong tu NE la tiep tuyen (O) =>$NE\perp DE$ Suy ra MD//NE ( Quan he tu vuong goc den song song)b) Noi NO , Goi F la trung diem OHXet $\Delta AHC$ co OH=OA ( gt) , HN=NC (gt)=> ON la duong trung binh => ON//ACma AB $AB\perp AC\left(\Delta ABCvuong\right)$Suy ra $NO\perp AB$Xet tam giac ABN co $AH\perp BN\left(gt\right),NO\perp AB\left(cmt\right)$ => O la truc tam tam giac ABN=> $BO\perp AN$ (1)Xet tam giac giac BHO co M la trung diem BH (gt) , F la trung diem OH ( gt)=> MF la duong trung binh => MF//BO (2)Tu (1) va (20 suy ra $MF\perp AN$ (quan he tu vuong goc den song song)Xet tam giac AMN co $\hept{\begin{cases}AH\perp MN\left(gt\right)\MF\perp AN\left(cmt\right)\end{cases}\Rightarrow}$ Trung diem F cua OH la truc tam $\Delta AMN$c) Xet tam giac ABH co AM la duong trung tuyen =>Samh =Sabm ( t/c trug tuyen chia cat doi dien thang 2 phan co dien h bag nhau)=> Samh=1/2Sabhtuong tu ta cung co Sahn = 1/2 SahcSuy ra Samh+Sahn =1/2 (Sabh +Sahc) <=> Samn=1/2 Sabc=> Samn min <=> Sabc minTheo minh thi tam giac ABC can co dk la dien h tam giac ABC nho nhat thi Samn dat gtnnMik ko chac cau c) lam dau. Neu sai mong cac bn thong cam ma sua ho mik,Mik cam on.Chuc ban hoc tot

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