Dinh ly : Trong mot tam giac bat ki thi khoang cach tu truc tam den dinh = 2 lan khoang cach tam duong tro ngoai tiep den canh doi dien.
Ap dung bo de vao bai nay goi giao 2 duong cheo hinh thoi la E thi : \(\frac{AH}{OE}=2\)
Noi AO,Tu K ke KI,KJ vuong goc voi BH,HC. Ta phai chung minh I,J la trung diem cua BH,HC la xong
That vay : Do O la giao 3 duong trung truc tam giac ABC => AO=BO=OC (1)
Do BOCK la hinh thoi nen OK =2OE ma AH=2OE (theo bo de) => AH=OK
Xet tu giac AHKO co :\(\hept{\begin{cases}AH//OK\left(\perp BC\right)\\AH=OK\left(=2OE\right)\end{cases}\Rightarrow}\) AHKE la hinh binh hanh => HK=AO
Suy ra HK=BO=OC=BK=KC (Do (1) va BOCK la hinh thoi)
Suy ra HK=BK,HK=KC =>\(\Delta KHBva\Delta KHC\) can tai K
Ma chung co cac duong cao la KI va KJ
Suy ra I,J la trung diemBH,HC => DPCM
neu ban ko biet dinh ly nay thi nt mik mik chi cach c/m cho
