Question

⊙v ≅ ⊙u. what is the length of \\(\overline{st}\\)?
(image of two circles: left circle u with chord st and a 74° arc, right circle v with chord qr (length 28) and a 286° arc)
st = \\(\square\\)

Explanation:

Step1: Find the measure of the arc corresponding to chord \(QR\)

The measure of the arc corresponding to chord \(QR\) is \(360^{\circ}- 286^{\circ}=74^{\circ}\)

Step2: Use the property of congruent circles

Since \(\odot V\cong\odot U\), chords subtending equal arcs in congruent circles are equal.
Chord \(ST\) in \(\odot U\) and chord \(QR\) in \(\odot V\) subtend arcs of measure \(74^{\circ}\)
So \(ST = QR\)

Answer:

\(28\)