# Difference between revisions of "2011 IMO Problems/Problem 6"

Humzaiqbal (talk | contribs) (Created page with "Let ABC be an acute triangle with circumcircle Γ. Let l be a tangent line to Γ, and let la, lb and lc be the lines obtained by reflecting l in the lines BC, CA and AB, respecti...") |
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− | Let ABC be an acute triangle with circumcircle | + | 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>. |

## Revision as of 13:34, 27 November 2011

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 .