Question

given the circle below with chords (overline{st}) and (overline{uv}). find the length of (overline{vw}). round to the nearest tenth if necessary.

Explanation:

Step1: Apply the intersecting chords theorem

When two chords \(ST\) and \(UV\) intersect at a point \(W\) inside a circle, the following relationship holds: \(UW\times WV=TW\times WS\). Let \(WV = x\). We know that \(UW = 33\), \(TW=36\), and \(WS = 28\).

Step2: Substitute the values into the formula

Substituting the values into the formula \(33x=36\times28\).

Step3: Solve for \(x\)

First, calculate \(36\times28 = 1008\). Then, we have the equation \(33x=1008\). Solving for \(x\), we get \(x=\frac{1008}{33}\approx40.1\).

Answer:

\(40.1\)