INMO 1995 Problem 4

Let $ABC$ be a triangle and a circle $\Gamma'$ be drawn lying outside the triangle, touching its incircle $\Gamma$ externally, and also the two sides $AB$ and $AC$ . Show that the ratio of the radii of the circles $\Gamma'$ and $\Gamma$ is equal to $\tan^ 2 { \left( \dfrac{ \pi - A }{4} \right) }.$