The value of x and the length of each chord is x = 9.1, AB = 16.5, CD = 14.1. Thus first option is correct.
What is the relation between line perpendicular to chord from the center of circle?
If the considered circle has center O and chord AB, then if there is perpendicular from O to AB at point C, then that point C is bisecting(dividing in two equal parts) the line segment AB.
Or
|AC| = |CB|
Let x be the measure of the length of ED.
[tex]5 \times x = 13 \times3.5\\5x = 45.5\\x = 9.1[/tex]
Therefore,
AB = 3.5 + 13 = 16.5
CD = 5 + 9.1 = 14.1
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