Question

given the circle below with chords vw and xy. find the length of yz. round to the nearest tenth if necessary.

Explanation:

Step1: Apply the intersecting chords theorem

When two chords \(XY\) and \(VW\) intersect at a point \(Z\) inside a circle, the following relationship holds: \(XZ\times ZY = VZ\times ZW\). Let \(ZY = x\). We know that \(XZ = 21\), \(VZ=15\), and \(ZW = 15\).

Step2: Substitute values into the formula

Substitute the values into the formula \(21x=15\times15\). So, \(21x = 225\).

Step3: Solve for \(x\)

To find \(x\), we use the equation \(x=\frac{225}{21}\). Calculate \(\frac{225}{21}\approx10.7\) (rounded to the nearest tenth).

Answer:

\(10.7\)