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Inscribed and Circumscribed Circles
Two tangents drawn from one point
[The area of a figure is equal to the sum of the areas of the figures into which it is divided]

On the sides $B C, C A$, and $A B$ of a triangle, points $A_{1}, B_{1}, C_{1}$ are taken respectively, such that the radii of the circles inscribed in triangles $A_{1} B C_{1}, A B_{1} C_{1}$, and $A_{1} B_{1} C$ are equal to each other and equal to $r$. The radius of the circle inscribed in triangle $A_{1} B_{1} C_{1}$ is $r_{1}$. Find the radius of the circle inscribed in triangle $A B C$.

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