a, - Xét \(\Delta IKC\) và \(\Delta ICB\) có :
\(\left\{{}\begin{matrix}\widehat{KIC}\left(chung\right)\\\widehat{ICK}=\widehat{IBC}\left(=\frac{1}{2}Sđ\stackrel\frown{KC}\right)\end{matrix}\right.\)
=> \(\Delta IKC\) ~ \(\Delta ICB\) ( g - g )
=> \(\frac{IK}{IC}=\frac{IC}{IB}\)
=> \(IC^2=IK.IB\left(đpcm\right)\)
b, Ta có : BD // AC .
=> \(\widehat{BDA}=\widehat{DAC}\) ( So le trong )
Mà \(\widehat{BDA}=\widehat{ABI}\left(=\frac{1}{2}Sđ\stackrel\frown{BK}\right)\)
=> \(\widehat{DAC}=\widehat{ABI}\) .
- Xét \(\Delta AIK\) và \(\Delta BIA\) có :
\(\left\{{}\begin{matrix}\widehat{AIB}\left(chung\right)\\\widehat{DAI}=\widehat{ABI}\left(cmt\right)\end{matrix}\right.\)
=> \(\Delta AIK\) ~ \(\Delta BIA\) ( g - g )
=> \(\frac{AI}{IK}=\frac{IB}{AI}\)
=> \(AI^2=IK.IB\)
Mà \(IC^2=IK.IB\) ( câu a )
=> \(AI=IC\left(đpcm\right)\)
c, not hiểu câu hỏi