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

Answer 1

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

`AE* EB=CE* ED\\\\\Rightarrow 9*21=12* x\\\\\Rightarrow x=(9* 21)/(12)\\\\\\\Rightarrow x=(63)/(4)\\\\\Rightarrow x=15.75.`

Rounding to the nearest tenth, we get

x = 15.8 units.

Thus, the value of x is 15.8 units.

Option (A) is CORRECT.