Question

question 5 of 5
type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.
in circle c, ( pr = 4 ), ( qr = 5 ), and ( rt = 15 ). what is ( rs )?
( rs=square )

Explanation:

Step1: Use the intersecting chords theorem

If two chords \(PQ\) and \(TS\) intersect at a point \(R\) inside a circle, then \(PR\times RQ=SR\times RT\).
Given \(PR = 4\), \(QR=5\), and \(RT = 15\). Let \(RS=x\).
Substitute the values into the formula: \(4\times5=x\times15\).

Step2: Solve the equation for \(x\)

We have the equation \(20 = 15x\).
Divide both sides by 15: \(x=\frac{20}{15}=\frac{4}{3}\).

Answer:

\(\frac{4}{3}\)