Question

5
find the length of the segment indicated. round your answer to the nearest tenth if necessary.
10.4
10.4
6.1
x
8.4

Explanation:

Step1: Apply chord-segment theorem

When two chords intersect in a circle, the products of the lengths of their segments are equal: $10.4 \times 10.4 = 6.1 \times (8.4 + x)$

Step2: Calculate left-hand side

Compute the product of the diameter segments:
$10.4^2 = 108.16$

Step3: Isolate the parenthetical term

Rearrange to solve for $(8.4 + x)$:
$8.4 + x = \frac{108.16}{6.1}$
$8.4 + x \approx 17.731$

Step4: Solve for $x$

Subtract 8.4 from both sides:
$x \approx 17.731 - 8.4$
$x \approx 9.3$

Answer:

$9.3$