ent to the circle centered at o. given that jl = 8.4 and oj = 11.6, find ok.
ok =

Question

Accepted Answer

# Explanation:
## Step1: Use the property of tangent to circle
Since $JL$ is tangent to the circle at $L$, $OL\perp JL$ (tangent to a circle is perpendicular to the radius at the point of tangency). So, $\triangle OJL$ is a right - triangle with $OJ$ as the hypotenuse. Let $OL = OK$ (radii of the same circle).
## Step2: Apply the Pythagorean theorem
In right - triangle $\triangle OJL$, by the Pythagorean theorem $OL^{2}+JL^{2}=OJ^{2}$. Let $OL = r$, then $r^{2}+8.4^{2}=11.6^{2}$.
$$
\begin{align*}
r^{2}&=11.6^{2}-8.4^{2}\
r^{2}&=(11.6 + 8.4)(11.6-8.4)\
r^{2}&=(20)\times(3.2)\
r^{2}&=64\
r& = 8
\end{align*}
$$

# Answer:
$OK = 8$

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QUESTION IMAGE

Question

Explanation:

Step1: Use the property of tangent to circle

Step2: Apply the Pythagorean theorem

Answer: