in the figure to the right, if ( ac = 16 ) and ( bc = 13 ), what is the radius?
the radius is approximately ( square ). (round to the nearest tenth as needed.)

Question

Accepted Answer

# Explanation:
## Step1: Let the radius $AB = AD = r$
Since $AB$ and $AD$ are radii of the circle.
## Step2: Apply the Pythagorean theorem in $\triangle ABC$
In right - triangle $ABC$, by the Pythagorean theorem $AB^{2}+BC^{2}=AC^{2}$. Substituting $AB = r$, $BC = 13$, and $AC = 16$, we get $r^{2}+13^{2}=16^{2}$.
## Step3: Solve for $r$
$$
\begin{align*}
r^{2}&=16^{2}-13^{2}\
r^{2}&=256 - 169\
r^{2}&=87\
r&=\sqrt{87}\
r&\approx9.3
\end{align*}
$$

# Answer:
$9.3$

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QUESTION IMAGE

Question

Explanation:

Step1: Let the radius \(AB = AD = r\)

Step2: Apply the Pythagorean theorem in \(\triangle ABC\)

Step3: Solve for \(r\)

Answer: