Difference between revisions of "2006 Canadian MO Problems/Problem 5"

 
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The vertices of right triangle <math>ABC</math> inscribed in a circle divide the three arcs, we draw a tangent intercepted by the lines <math>AB</math> and <math>AC</math>. If the tangency points are <math>D</math>, <math>E</math>, and <math>F</math>, show that the triangle <math>DEF</math> is equilateral.
 
The vertices of right triangle <math>ABC</math> inscribed in a circle divide the three arcs, we draw a tangent intercepted by the lines <math>AB</math> and <math>AC</math>. If the tangency points are <math>D</math>, <math>E</math>, and <math>F</math>, show that the triangle <math>DEF</math> is equilateral.
 
==Solution==
 
==Solution==
 
 
{{solution}}
 
{{solution}}
  
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==See also==
 
*[[2006 Canadian MO]]
 
*[[2006 Canadian MO]]
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{{CanadaMO box|year=2006|num-b=4|after=Last question}}

Revision as of 18:58, 7 February 2007

Problem

The vertices of right triangle $ABC$ inscribed in a circle divide the three arcs, we draw a tangent intercepted by the lines $AB$ and $AC$. If the tangency points are $D$, $E$, and $F$, show that the triangle $DEF$ is equilateral.

Solution

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See also

2006 Canadian MO (Problems)
Preceded by
Problem 4
1 2 3 4 5 Followed by
Last question