2015 OIM Problems/Problem 2: Difference between revisions
Created page with "== Problem == A line <math>r</math> contains the points <math>A</math>, <math>B</math>, <math>C</math> and <math>D</math> in that order. Let <math>P</math> be a point outside..." |
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== See also == | == See also == | ||
[[OIM Problems and Solutions]] | |||
Latest revision as of 14:05, 14 December 2023
Problem
A line 
contains the points 
, 
, 
and 
in that order. Let 
be a point outside of such that 
. Prove that the bisector of 
cuts at a point 
such that
![\[\frac{1}{GA}+\frac{1}{GC}=\frac{1}{GB}+\frac{1}{GD}\]](http://latex.artofproblemsolving.com/0/e/9/0e96628b9cde3206ad485a3ca67769a739bdde9d.png)
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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