8,9}

In triangle $A B C$, angle $A$ is equal to $\arccos \frac{5}{13}$, side $B C$ is equal to 12. On the extension of $C B$ beyond point $C$, a point $M$ is taken such that $C M=6$. Find the radius of the circle passing through vertex $A$, tangent to line $B C$ at point $M$, and tangent to the circumcircle of triangle $A B C$.
![](https://cdn.mathpix.com/cropped/2024_05_06_08de36b0d140fd8f2c0dg-36.jpg?height=638&width=1146&top_left_y=2122&top_left_x=502)

## Answer

6.00

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