14 multiple choice 1 point

in the diagram above, $ \overline { p a } $ is tangent to circle $ o $. if $ p a = 15 $ and $ o p = 20 $, find the radius of circle $ o $. if your answer is not an integer, round to the nearest tenth.
12.6
14.4
13.2
13.8

Question

14 multiple choice 1 point

in the diagram above, $ \overline { p a } $ is tangent to circle $ o $. if $ p a = 15 $ and $ o p = 20 $, find the radius of circle $ o $. if your answer is not an integer, round to the nearest tenth.
12.6
14.4
13.2
13.8

Accepted Answer

# Explanation:
## Step1: Use the property of tangent to a circle
A tangent to a circle is perpendicular to the radius at the point of tangency. So, $\angle OAP = 90^{\circ}$, and $\triangle OAP$ is a right - triangle.
## Step2: Apply the Pythagorean theorem
In right - triangle $\triangle OAP$, by the Pythagorean theorem $OA^{2}+PA^{2}=OP^{2}$. Let $OA = r$ (radius of the circle). We know $PA = 15$ and $OP = 20$. Then $r^{2}+15^{2}=20^{2}$.
## Step3: Solve for $r$
$$
\begin{align*}
r^{2}&=20^{2}-15^{2}\
r^{2}&=400 - 225\
r^{2}&=175\
r&=\sqrt{175}\
r&=\sqrt{25\times7}\
r& = 5\sqrt{7}\approx5\times2.646\
r&\approx13.2
\end{align*}
$$

# Answer:
13.2

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QUESTION IMAGE

Question

Explanation:

Step1: Use the property of tangent to a circle

Step2: Apply the Pythagorean theorem

Step3: Solve for \(r\)

Answer: