Problem 4. On the segment $AC$, point $B$ is marked. On the segments $AB$, $BC$, and $AC$, as diameters, semicircles are constructed in the same half-plane. A circle with center at point $O$ is tangent to all these semicircles (see figure). Find the radius of this circle if $AB=4$, $BC=2$. If necessary, round the answer to 0.01.

![](https://cdn.mathpix.com/cropped/2024_05_06_3d56dfe007823ba1bf39g-1.jpg?height=380&width=728&top_left_y=1346&top_left_x=664)
Answer: $6 / 7 \approx 0.86$.