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

(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 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, respectively. Show that the circumcircle of the triangle determined by the lines la, lb and lc is tangent to the circle Γ.
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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>.

Revision as of 13:34, 27 November 2011

Let $ABC$ be an acute triangle with circumcircle $\Gamma$. Let $\ell$ be a tangent line to $\Gamma$, and let $\ell_a, \ell_b$ and $\ell_c$ be the lines obtained by reflecting $\ell$ in the lines $BC$, $CA$ and $AB$, respectively. Show that the circumcircle of the triangle determined by the lines $\ell_a, \ell_b$ and $\ell_c$ is tangent to the circle $\Gamma$.

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