A circle which is tangent to the sides $ [AB]$ and $ [BC]$ of $ \triangle ABC$ is also tangent to its circumcircle at the point $ T$. If $ I$ is the incenter of $ \triangle ABC$ , show that $ \widehat{ATI}=\widehat{CTI}$
Dear Mathlinkers,
your circle is a mixtilinear incircle.
A proof can be seen on
http://perso.orange.fr/jl.ayme vol. 4 A new mixtilinear incircle adventure p. 17-18 (in french)
Sincerely
Jean-Louis
sinankaral53 wrote:
A circle which is tangent to the sides $ [AB]$ and $ [BC]$ of $ \triangle ABC$ is also tangent to its circumcircle at the point $ T$. If $ I$ is the incenter of $ \triangle ABC$ , show that $ \widehat{ATI} = \widehat{CTI}$
It is a nice problem(probably an IMO short list) but I can not find where we have discussed it here ! If someone has the
link, please send it!
Mmm ! I found one :
http://www.mathlinks.ro/viewtopic.php?search_id=647921583&t=31739
but it is also discussed and some where else.
Babis