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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