1. Statement of the problem: In the given figure the lengths of paths AMB, circular path AB and ARB are $D_1$, $D_2$ and $D_3$ respectively, and we must choose the correct option. 2. Coordinate model: Take the square side length 2 with $A=(0,0)$, $M=(2,0)$, $B=(2,2)$, O at $(0,2)$, midpoints $P=(0,1)$, $Q=(1,2)$ and $R=(1,1)$. 3. Compute $D_1$: Path AMB is the polyline $A\to M\to B$ so $D_1=AM+MB$. 4. Compute $AM$ and $MB$: $AM=2$ and $MB=2$ so $D_1=2+2=4$. 5. Compute $D_2$: Circular path $AB$ is a quarter-circle of radius $2$ so $D_2=\frac{1}{4}\cdot 2\pi\cdot 2=\pi$. 6. Compute $D_3$: Path $A\to R\to B$ has $AR=RB=\sqrt{(1-0)^2+(1-0)^2}=\sqrt{2}$ so $D_3=2\sqrt{2}$. 7. Numerical approximations: $D_1=4$, $D_2=\pi\approx 3.1416$, $D_3=2\sqrt{2}\approx 2.8284$. 8. Comparison and conclusion: Therefore $D_1>D_2>D_3$ and the correct option is (A) $D_1>D_2>D_3$.