Answer: The correct option is (A) x = 15.8 units.
Step-by-step explanation: As given in the question, the chords AB and CD of a circle intersect at the point E. See the modified attached figure.
Also, AE = 9 units, EB = 21 units, CE = 12 units and ED = x.
We are to find the value of x.
Chord Intersecting Theorem: This theorem gives a relation of the four line segments created by two intersecting chords in a circle, which states that the products of the lengths of the line segments on each chord are equal.
Applying the above theorem in the given situation, we can write
[tex]AE\times EB=CE\times ED\\\\\Rightarrow 9\times21=12\times x\\\\\Rightarrow x=\dfrac{9\times 21}{12}\\\\\\\Rightarrow x=\dfrac{63}{4}\\\\\Rightarrow x=15.75.[/tex]
Rounding to the nearest tenth, we get
x = 15.8 units.
Thus, the value of x is 15.8 units.
Option (A) is CORRECT.
