1. Stating the problem: In the given figure the lengths of paths AMB, circular path AB and ARB are $D_1$, $D_2$, $D_3$ respectively, and you asked to choose the correct option. 2. Missing information: The figure and the answer choices are not provided, so the single correct option cannot be determined from the text alone. 3. Definitions and assumptions: I assume AMB denotes the broken path from A to B via M, so $D_1=|AM|+|MB|$ is the sum of two straight segments. I assume $D_2$ denotes the arc length of AB along the circle. I assume $D_3$ denotes the other circular path ARB (the complementary arc) if that is the intended meaning. 4. Useful inequalities: By the triangle inequality the broken path satisfies $D_1\u2265 |AB|$, with equality only when M lies on the segment AB. An arc length is at least the chord length, so $D_2\u2265 |AB|$, with strict inequality for distinct A,B on the circle. If $D_2$ is the minor arc and $D_3$ the major arc then $D_3>D_2$ and $D_2+D_3=C$ where $C$ is the circumference of the circle. 5. Common comparisons you can often choose from: Without the figure you can deduce $|AB|\le \min(D_1,D_2)$. If the question is to order the three lengths typical answers are $|AB|\le D_1$ and $|AB|\le D_2$ and either $D_2D_3$ depending on which is minor. 6. Conclusion and request: Please provide the figure or list the answer options so I can select the correct option and show full working.