1)
Xet tam giac AIE co:
goc AIE=(sd cung BD+sd cung AE):2 (tinh chat goc co dinh nam trong duong tron)
ma: sd cung BD=sd cung DC (vi AD la phan giac cua goc BAC)
sd cung AE=sd cung EC (vi BE la phan giac goc ABC)
=>goc AIE=(sd cung DC+sd cung EC):2=(sd cung CE):2
lai co: goc DAE=(sd cung DE):2
Suy ra : goc AIE=goc DAE
=> tam giac AIE can tai E
Chung minh tuong tu ta cung co: tam giac BDI can tai D
2)
Ta co: goc AME=(sd cung AE+sd cung DC):2 (tinh chat cua goc co dinh nam trong duong tron)
=>goc AME=(sd cung AE+sd cung BD):2 (vi sd cung BD=sd cung CD)
Ma: goc AIE=(sd cung AE+sd cung BD):2
Suy ra: goc AIE=goc AME
=>tu giac AIEM noi tiep duoc duong tron
=>goc MAE=goc MIE
Ta lai co: goc EBC=goc CAE=(sd cung EC):2
Suy ra: goc MIE=goc EBC
=>MI//BC (vi co 2 goc bang nhau o vi tri dong vi)
3)
Tu giac BIND co:
goc BID=(sd cung AE+sd cung BD):2=(sd cung EC+sd cung BD):2
ma: goc BND=(sd cung EC+sd cung BD):2
=>goc BID=goc BND => tu giac BIND noi tiep => goc INB=goc BDI hay goc BNI=goc BDA=goc BCA
=>IN//CM (vi co 2 goc bang nhau o vi tri dong vi)
Tu giac CMIN co:
IN//CM (chung minh tren)
IM//NC (vi IM//BC;N thuoc BC)
=>tu giac CMIN la hinh binh hanh
Xet tam giac CMN co:
goc CNM=(sd cung EC+sd cung BD):2=(sd cung AE+sd cung DC):2
ma goc CMN=(sd cung AE+sd cung DC):2
=> goc CNM=goc CMN
Suy ra: tam giac CMN can tai C=> CN=CM
Hinh binh hanh CMIN co: CN=CM (chung minh tren)
=>CMIN la hinh thoi
MONKEY_MINH_96 OI! NHU ZAY LA OK ZUI DAY. AK! DO BAN DANG NHAP CUNG NGAY CUNG THANG CUNG NAM VOI MINH NEN MINH MOI GIAI BAI TOAN NAY GIUP DAY.HJHJHJHJHJHJHJ co hoc dj de do cap 3 nha^_^>:
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