Difference between revisions of "2020 USAMO Problems/Problem 1"
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+ | ==Problem 1== | ||
+ | Let <math>ABC</math> be a fixed acute triangle inscribed in a circle <math>\omega</math> with center <math>O</math>. A variable point <math>X</math> is chosen on minor arc <math>AB</math> of <math>\omega</math>, and segments <math>CX</math> and <math>AB</math> meet at <math>D</math>. Denote by <math>O_1</math> and <math>O_2</math> the circumcenters of triangles <math>ADX</math> and <math>BDX</math>, respectively. Determine all points <math>X</math> for which the area of triangle <math>OO_1O_2</math> is minimized. | ||
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==Video Solution== | ==Video Solution== | ||
https://www.youtube.com/watch?v=m157cfw0vdE | https://www.youtube.com/watch?v=m157cfw0vdE |
Revision as of 15:21, 15 September 2022
Problem 1
Let be a fixed acute triangle inscribed in a circle
with center
. A variable point
is chosen on minor arc
of
, and segments
and
meet at
. Denote by
and
the circumcenters of triangles
and
, respectively. Determine all points
for which the area of triangle
is minimized.