Question

question 5 of 5
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in circle c, pr = 4, qr = 6, and rt = 16. what is rs?
rs =
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Explanation:

Step1: Apply the intersecting chords theorem

If two chords \(AB\) and \(CD\) intersect at a point \(R\) inside a circle, then \(PR\times RT=QR\times RS\).
Given \(PR = 4\), \(QR=6\), \(RT = 16\). Let \(RS=x\).
Substitute the values into the formula: \(4\times16=6\times x\).

Step2: Solve the equation for \(x\)

The equation \(4\times16 = 6x\) simplifies to \(64=6x\).
Then \(x=\frac{64}{6}=\frac{32}{3}\approx10.67\).

Answer:

\(\frac{32}{3}\)