Question

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

Explanation:

Step1: Apply chord intersection theorem

When two chords intersect in a circle, the products of the lengths of their segments are equal: $QU \times TU = SU \times RU$

Step2: Substitute known values

$6 \times TU = 4 \times 7$

Step3: Calculate right-hand side

$4 \times 7 = 28$

Step4: Solve for $TU$

$TU = \frac{28}{6} \approx 4.7$

Answer:

4.7