Difference between revisions of "2022 OIM Problems/Problem 1"
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== Problem == | == 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> | + | 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 == | == Solution == | ||
Latest revision as of 03:29, 14 December 2023
Problem
Let 
be an equilateral triangle with circumcenter 
and circumcircle 
. Let 
be a point on the minor arc 
, with 
. The perpendicular bisector of 
intersects at 
and 
, with on the minor arc . Let 
be the intersection point of lines 
and 
. Prove that 
is perpendicular to .
Solution
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