Olympiad Geometry Problem #100: Circumcenter Perpendiculars Cyclic Quad

Here is a tremendous problem from the 2010 Kazakhstan Math Olympiad, recommended to me by another subscriber on my channel. It was a nice challenge, although still probably easier than some of my more recent videos. Enjoy! Link below.

[kamranmehdiyev]

Cool, a minor detail, the first cross ratio you mentioned is equal to (-1) not 1, the reason is that in projective geometry we take the harmonic ratio (AB;CD)=-1 when the segments AB, CD have common point and 1 otherwise .
I agree that working backwards helps here

[omparkash-njzy]

Congratulations for century. All hundred are unique and well explained, with elegant solution.
Keep it up. 👍

[drozfarnyline]

You are right!
The Problem is still valid if O lies on the perpendicular bisector of BC!

[vtk]

could you make some more video about some topics like harmonic; poles and polars. Thank you

[ИбадатЖұмабек]

Керемет 2009-2010 оқу жылы 11-класс 5- тапсырма / сізге рахмет

[ramswaroopmohanty]

U could use power of a point and symilarity with the same construction u had done to proceed further....i had done done the exact same construction

[mathematicalolympiad]

Could you make some videos about inversion please 😊

[sumanpandey]

Sir please start geometry full length video for imo