Olympiad Geometry Problem #41: Mixtilinear Incircles

Here is a very useful configuration in many geometry problems, even those which don't explicitly state that they involve mixtilinear incircles. I'm following the exposition from a free ebook called A Beautiful Journey in Olympiad Geometry (which has a suggested donation). Enjoy!

[chaitanyagaur]

There were very less resources for IMO preparation back then.
There are no mathematical circles in India and no teahcers who can teach olympiad type problem.s Nobody really knows whats IMO.
But youtube channels like these are democratzing olympiad resources for everyone.

Thanks a lot!

[giakhanhphan]

You should keep doing this more often! I like this channel

[asmaehiba]

Thank you Michael for your time and your efforts 💫💫

[yashvardhan]

If we study the curvilinear in circles before it we can conclude things like the cyclicity of FBTI and the midpoints of arcs more quickly

[chetdivedau]

Awesome! By Archimedes Lemma we get that points T, F, E and T, G, D are collinear. 🤗

[prithujsarkar]

Hi michael, can you make a video on curvilinear incircles too? its not a very famous config(atleast not as famous as the mixtilinear incircle, that's the reason im requesting this) and can be found on egmo ch4 (if i remember correctly)

[lesliegiancarlo]

could you do a video that prove this using inversion about A with radius sqrt(AB*AC)?

[beautifulworld]

Beautiful journey through geometry 📐 ( stefan lozanovski) is very nice book