Difference between revisions of "2023 USAMO Problems/Problem 6"
(Created page with "== Problem == Let ABC be a triangle with incenter <math>I</math> and excenters <math>I_a</math>, <math>I_b</math>, <math>I_c</math> opposite <math>A</math>, <math>B</math>, an...") |
(→Solution) |
||
Line 3: | Line 3: | ||
== Solution == | == Solution == | ||
{{Solution}} | {{Solution}} | ||
+ | |||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 19:59, 9 May 2023
Problem
Let ABC be a triangle with incenter and excenters
,
,
opposite
,
, and
, respectively. Given an arbitrary point
on the circumcircle of
that does not lie on any of the lines
,
, or
, suppose the circumcircles of
and
intersect at two distinct points
and
. If
is the intersection of lines
and
, prove that
.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.