Difference between revisions of "2017 USAMO Problems/Problem 3"
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| + | Let <math>ABC</math> be a scalene triangle with circumcircle <math>\Omega</math> and incenter <math>I.</math> Ray <math>AI</math> meets <math>BC</math> at <math>D</math> and <math>\Omega</math> again at <math>M;</math> the circle with diameter <math>DM</math> cuts <math>\Omega</math> again at <math>K.</math> Lines <math>MK</math> and <math>BC</math> meet at <math>S,</math> and <math>N</math> is the midpoint of <math>IS.</math> The circumcircles of <math>\triangle KID</math> and <math>\triangle MAN</math> intersect at points <math>L_1</math> and <math>L.</math> Prove that <math>\Omega</math> passes through the midpoint of either <math>IL_1</math> or <math>IL.</math> | ||
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Revision as of 17:54, 20 September 2022
Let 
be a scalene triangle with circumcircle 
and incenter 
Ray 
meets 
at 
and again at 
the circle with diameter 
cuts again at 
Lines 
and meet at 
and 
is the midpoint of 
The circumcircles of 
and 
intersect at points 
and 
Prove that passes through the midpoint of either 
or 
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