Question

chords tv and su intersect inside the circle at point r.
rt = 5
rv = 8
rs = 4
what is the length of \overline{ru}?
a 2.5
b. 7.0
c 6.4
d. 10.0

Explanation:

Step1: Use the intersecting chords theorem

When two chords intersect inside a circle, \(RT\times RV=RS\times RU\).

Step2: Substitute the known values

Given \(RT = 5\), \(RV=8\), \(RS = 4\). Let \(RU=x\). Then \(5\times8=4\times x\).

Step3: Solve for \(x\)

We have the equation \(40 = 4x\). Divide both sides by 4: \(x=\frac{40}{4}=10\).

Answer:

D. 10.0