A wire of uniform resistance λ / m is bent into a circle of radius...

The wire bent into a circle of radius $r$ has resistance $\lambda \cdot \pi r$ for the semicircular arcs, and the straight wire of length $2r$ has resistance $\lambda \cdot 2r$. The three paths between A and B (two semicircular arcs of the circle and one straight wire through center) are in parallel.

$\frac{1}{R_{AB}} = \frac{2}{\lambda \pi r} + \frac{1}{\lambda \cdot 2r} + \frac{2}{\lambda \cdot 3\pi r}$

$= \frac{1}{\lambda r} \left[\frac{2}{\pi} + \frac{1}{2} + \frac{2}{3\pi}\right]$

$= \frac{1}{\lambda r} \left(\frac{12 + 3\pi + 4}{6\pi}\right) = \frac{1}{\lambda r} \cdot \frac{16 + 3\pi}{6\pi}$

$R_{AB} = \lambda r \left(\frac{6\pi}{16 + 3\pi}\right) = \frac{6\pi \lambda r}{3\pi + 16}$