The distance between two parallel chords, each of length $10$ units is $24$ units then the radius of the circle is:

Assuming the parallel chords are on opposite sides of the center, their distances from the center are found using the Pythagorean theorem. For a chord of length 10, the half-length is 5, so the distance from the center is $\sqrt{r^2 - 25}$. Since the total distance is 24, the distances from the center must be 12 each, meaning $\sqrt{r^2 - 25} = 12$. Solving this yields $r^2 - 25 = 144$, so $r^2 = 169$ and the radius is 13.

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