Question

Answer 1

Xét \(\Delta ABC\) có: \(AC>BC>AB\) 

=> \(\widehat{ABC}>\widehat{BAC}>\widehat{ACB}\)

\(\Rightarrow\)\(\dfrac{\widehat{ABC}}{2}>\dfrac{\widehat{BAC}}{2}>\dfrac{\widehat{ACB}}{2}\)

Xét \(\Delta IAC\) có: \(\widehat{IAC}>\widehat{ICA}\) (\(\dfrac{\widehat{BAC}}{2}>\dfrac{\widehat{ACB}}{2}\)  )

=> IC>IA(1)

Xét \(\Delta IAB\) có: \(\widehat{IBA}>\widehat{IAB}\) (\(\dfrac{\widehat{ABC}}{2}>\dfrac{\widehat{BAC}}{2}\))

=> IA>IB(2)

Từ (1)(2)=> IC>IA>IB