Question

given the circle below with chords \\( \overline{v w} \\) and \\( \overline{x y} \\). find the length of \\( \overline{y z} \\). round to the nearest tenth if necessary.

Explanation:

Step1: Apply the Chord - Chord Product Theorem

If two chords \(VW\) and \(XY\) intersect at a point \(Z\) inside a circle, then \(VZ\times ZW=XZ\times ZY\).
Let \(VZ = 15\), \(ZW=15\), \(XZ = 21\), and \(ZY=x\).
The formula becomes \(15\times15=21\times x\).

Step2: Solve for \(x\)

We have the equation \(225 = 21x\).
Dividing both sides by \(21\), we get \(x=\frac{225}{21}\approx10.7\).

Answer:

\(10.7\)