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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