Mathematics

Question

A circle with two chords is shown below. The diagram is not drawn to scale. What is the value of x? Round the answer to the nearest tenth.
A:x=15.8
B:x=5.1
C:x=189.0
D:x=28.0
A circle with two chords is shown below. The diagram is not drawn to scale. What is the value of x? Round the answer to the nearest tenth. A:x=15.8 B:x=5.1 C:x=

2 Answer

  • check the picture below

    use the theorem then, to see what "x" is
  • 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.

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