View source for 2022 OIM Problems/Problem 1

== Problem ==

Let <math>ABC</math> be an equilateral triangle with circumcenter <math>O</math> and circumcircle <math>\Gamma</math>. Let <math>D</math> be a point on the minor arc <math>BC</math>, with <math>DB > DC</math>. The perpendicular bisector of <math>OD</math> intersects <math>\Gamma</math> at <math>E</math> and <math>F</math>, with <math>E</math> on the minor arc <math>BC</math>. Let <math>P</math> be the intersection point of lines <math>BE</math> and <math>CF</math>.  Prove that <math>PD</math> is perpendicular to <math>BC</math>.

== Solution ==
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== See also ==
https://sites.google.com/uan.edu.co/oim-2022/inicio