# Difference between revisions of "2006 USAMO Problems/Problem 6"

Ragnarok23 (talk | contribs) |
Ragnarok23 (talk | contribs) |
||

Line 1: | Line 1: | ||

== Problem == | == Problem == | ||

+ | Let <math>ABCD</math> be a quadrilateral, and let <math>E</math> and <math>F</math> be points on sides <math>AD</math> and <math>BC</math> respectively, such that <math>\frac{AE}{ED}=\frac{BF}{FC}.</math> Ray <math>FE</math> meets rays <math>BA</math> and <math>CD</math> at <math>S</math> and <math>T</math> respectively. Prove that the circumcircles of triangles <math>SAE, SBF, TCF,</math> and <math>TDE</math> pass through a common point. | ||

== Solution == | == Solution == | ||

== See Also == | == See Also == | ||

*[[2006 USAMO Problems]] | *[[2006 USAMO Problems]] |

## Revision as of 12:09, 12 July 2006

## Problem

Let be a quadrilateral, and let and be points on sides and respectively, such that Ray meets rays and at and respectively. Prove that the circumcircles of triangles and pass through a common point.