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In triangle $ABC$, angle $B$ is equal to $\arccos \frac{15}{17}$. On side $AC$, a point $K$ is taken such that $AK=12$, $KC=4$. Find the radius of the circle passing through vertex $B$, touching side $AC$ at point $K$, and touching the circumcircle of triangle $ABC$.

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![](https://cdn.mathpix.com/cropped/2024_05_06_08de36b0d140fd8f2c0dg-36.jpg?height=1281&width=1286&top_left_y=0&top_left_x=432)

## Answer

12.00