<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 Inside the circle $\omega$ are two intersecting circles $\omega_{1}$ and $\omega_{2}$, which intersect at points $K$ and $L$, and are tangent to the circle $\omega$ at points $M$ and $N$. It turns out that the points $K$, $M$, and $N$ are collinear. Find the radius of the circle $\omega$, given that the radii of the circles $\omega_{1}$ and $\omega_{2}$ are 3 and 5, respectively. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
8
Inside the circle $\omega$ are two intersecting circles $\omega_{1}$ and $\omega_{2}$, which intersect at points $K$ and $L$, and are tangent to the circle $\omega$ at points $M$ and $N$. It turns out that the points $K$, $M$, and $N$ are collinear. Find the radius of the circle $\omega$, given that the radii of the circles $\omega_{1}$ and $\omega_{2}$ are 3 and 5, respectively.
test