Inside triangle
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
there are three circles
![k_1, k_2, k_3](/media/m/3/e/7/3e73f234287ee901415209a48a80c1a4.png)
each of which is tangent to two sides of the triangle and to its incircle
![k](/media/m/f/1/3/f135be660b73381aa6bec048f0f79afc.png)
. The radii of
![k_1, k_2, k_3](/media/m/3/e/7/3e73f234287ee901415209a48a80c1a4.png)
are
![1, 4](/media/m/8/e/8/8e889d1900ef4b001410d3bd7d56f0a4.png)
, and
![9](/media/m/7/f/0/7f02ff2403dbf63ddc4395762441de88.png)
. Determine the radius of
%V0
Inside triangle $ABC$ there are three circles $k_1, k_2, k_3$ each of which is tangent to two sides of the triangle and to its incircle $k$. The radii of $k_1, k_2, k_3$ are $1, 4$, and $9$. Determine the radius of $k.$