Answer: You are correct. AB is longer than DC.
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Explanation:
OM and ON are not equal in length, so the chords AB and CD are not the same length. The chords would need to be equally distant from the center for the chords to be equal.
The further a chord gets from the center, the smaller the chord gets. This is because the diameter is the largest chord possible and its distance from the center is 0 units. Increase that distance and the chord will shrink until it reaches 0 units in length.
You are correct in stating that AB is longer than DC because AB is closer to the center (or that OM is smaller than ON).
