Question

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

Explanation:

Step1: Apply the Chord - Chord Product Theorem

If two chords \(UV\) and \(WX\) intersect at a point \(Y\) inside a circle, then \(UY\times VY=WY\times XY\).
Let \(WY = x\). We know that \(UY = 10\), \(VY=5\), and \(XY = 9\).
The equation from the theorem is \(10\times5=x\times9\).

Step2: Solve for \(x\)

From \(10\times5=x\times9\), we have \(50 = 9x\).
Then \(x=\frac{50}{9}\approx5.6\)

Answer:

\(5.6\)