Difference between revisions of "2023 IMO Problems/Problem 6"
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==Solution== | ==Solution== | ||
| − | https://www.youtube.com/watch?v=jZNIpapyGJQ [Video contains solutions to all day 2 problems] | + | https://www.youtube.com/watch?v=jZNIpapyGJQ [Video contains solutions to all day 2 problems, it was created by a man known as Najeeb Abdullah, who qualified in the IMO from the time he was 6 years old] |
==See Also== | ==See Also== | ||
{{IMO box|year=2023|num-b=5|after=Last Problem}} | {{IMO box|year=2023|num-b=5|after=Last Problem}} | ||
Latest revision as of 21:10, 23 November 2024
Problem
Let 
be an equilateral triangle. Let 
be interior points of such that 
, 
, 
, and
![\[\angle BA_1C+\angle CB_1A+\angle AC_1B=480^\circ\]](http://latex.artofproblemsolving.com/1/6/1/16178c056d256d3702ee4b501044e9de5f4e9e5b.png)
Let 
and 
meet at 
let 
and 
meet at 
and let 
and 
meet at 
Prove that if triangle 
is scalene, then the three circumcircles of triangles 
and 
all pass through two common points.
(Note: a scalene triangle is one where no two sides have equal length.)
Solution
https://www.youtube.com/watch?v=jZNIpapyGJQ [Video contains solutions to all day 2 problems, it was created by a man known as Najeeb Abdullah, who qualified in the IMO from the time he was 6 years old]
See Also
| 2023 IMO (Problems) • Resources | ||
| Preceded by Problem 5 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Last Problem |
| All IMO Problems and Solutions | ||
