Difference between revisions of "2011 IMO Problems/Problem 6"
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Let <math>ABC</math> be an acute triangle with circumcircle <math>\Gamma</math>. Let <math>\ell</math> be a tangent line to <math>\Gamma</math>, and let <math>\ell_a, \ell_b</math> and <math>\ell_c</math> be the lines obtained by reflecting <math>\ell</math> in the lines <math>BC</math>, <math>CA</math> and <math>AB</math>, respectively. Show that the circumcircle of the triangle determined by the lines <math>\ell_a, \ell_b</math> and <math>\ell_c</math> is tangent to the circle <math>\Gamma</math>. | Let <math>ABC</math> be an acute triangle with circumcircle <math>\Gamma</math>. Let <math>\ell</math> be a tangent line to <math>\Gamma</math>, and let <math>\ell_a, \ell_b</math> and <math>\ell_c</math> be the lines obtained by reflecting <math>\ell</math> in the lines <math>BC</math>, <math>CA</math> and <math>AB</math>, respectively. Show that the circumcircle of the triangle determined by the lines <math>\ell_a, \ell_b</math> and <math>\ell_c</math> is tangent to the circle <math>\Gamma</math>. | ||
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| + | ==Solution== | ||
| + | {{solution}} | ||
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| + | ==See Also== | ||
| + | *[[2011 IMO Problems]] | ||
Revision as of 00:17, 11 October 2013
Let 
be an acute triangle with circumcircle 
. Let 
be a tangent line to , and let 
and 
be the lines obtained by reflecting in the lines 
, 
and 
, respectively. Show that the circumcircle of the triangle determined by the lines and is tangent to the circle .
Solution
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