Answer :

The value of the variable x in the diagram shown is 7. Option A

How to determine the value

The intersecting chords theorem or just the chord theorem is a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords within a circle.

It states that the products of the lengths of the line segments on each chord are equal.

Then, we have that;

x + 16 = 4x - 5

collect the like terms, we get;

x - 4x = -5 - 16

add the like terms

-3x = -21

Divide by the coefficient

x = 7

Learn more about chords at: https://brainly.com/question/13950364

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Answer for this question is x = 16