Question

select the correct answer.
what is the length of \\(\overline{rs}\\)?
figure not drawn to scale
a. 8
b. 10
c. 16
d. 20

Explanation:

Step1: Find circle radius

The diameter is $4 + 16 = 20$, so radius $r = \frac{20}{2} = 10$.
The distance from center to $RS$: $10 - 4 = 6$.

Step2: Use Pythagorean theorem

Let half of $RS$ be $x$. The radius is the hypotenuse:
$$x^2 + 6^2 = 10^2$$
$$x^2 = 100 - 36 = 64$$
$$x = \sqrt{64} = 8$$

Step3: Calculate full length of RS

$RS = 2x = 2 \times 8 = 16$

Answer:

C. 16