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.

finding the missing length of the chord using the intersecting chords theorem

Solution:

Let AB and CD be the chords intersecting at E.

From the Intersecting chords theorem, which states that “the products of the lengths of the line segments on each chord are equal”, 

AE × EB = CE × ED

9 × 21 = 12 × x

x = 189/12

x = 15.75

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.

Summary:

A circle with two chords as shown, the value of x is 15.75, using Intersecting chords theorem.

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