giúp nhanh tui với ạ chứ chiều là đi hok r
1: Xét ΔADC có OI//DC
nên \(\dfrac{OI}{DC}=\dfrac{AI}{AD}\)
Xét ΔDAB có OI//AB
nên \(\dfrac{OI}{AB}=\dfrac{DI}{DA}\)
\(\dfrac{OI}{DC}+\dfrac{OI}{AB}=\dfrac{DI}{DA}+\dfrac{AI}{DA}=\dfrac{DI+AI}{DA}=\dfrac{DA}{DA}=1\)
Xét ΔBDC có OK//DC
nên \(\dfrac{OK}{DC}=\dfrac{BK}{BC}\)
Xét ΔCAB có OK//AB
nên \(\dfrac{OK}{AB}=\dfrac{CK}{CB}\)
\(\dfrac{OK}{AB}+\dfrac{OK}{DC}=\dfrac{BK}{BC}+\dfrac{KC}{BC}=\dfrac{BK+KC}{BC}=\dfrac{BC}{BC}=1\)
2:
Ta có: \(\dfrac{OI}{AB}+\dfrac{OI}{CD}=1\)
=>\(OI\left(\dfrac{1}{AB}+\dfrac{1}{CD}\right)=1\)(1)
Ta có: \(\dfrac{OK}{AB}+\dfrac{OK}{CD}=1\)
=>\(OK\left(\dfrac{1}{AB}+\dfrac{1}{CD}\right)=1\)(2)
Từ (1) và (2) suy ra OI=OK
\(\dfrac{IK}{AB}+\dfrac{IK}{CD}\)
\(=\dfrac{2\cdot IO}{AB}+\dfrac{2\cdot IO}{CD}\)
\(=2\left(\dfrac{IO}{AB}+\dfrac{IO}{CD}\right)=2\)
=>\(\dfrac{1}{AB}+\dfrac{1}{CD}=\dfrac{2}{IK}\)
