We know that the chord is 25 units long.
Also, according to the image, side 18 and half of the given chord from a right triangle. Let's find the hypothenuse with Pythagorean's Theorem.
[tex]\begin{gathered} r^2=18^2+25^2 \\ r=\sqrt[]{324+625}=\sqrt[]{949} \end{gathered}[/tex]
Now, we use Pythagorean's theorem to find half of the chord x.
[tex]\begin{gathered} (\sqrt[]{949})^2=(\frac{x}{2})^2+18^2 \\ 949-324=(\frac{x}{2})^2 \\ 625=(\frac{x}{2})^2 \\ \frac{x}{2}=\sqrt[]{625}=25 \\ x=2\cdot25=50 \end{gathered}[/tex]
Therefore, x is 50 units long. A is the right answer.
