From a point $Q$, the length of the tangent to a circle is $24\text{ cm}$ and the distance of $Q$ from the centre is $25\text{ cm}$. The radius of the circle is

The radius to the point of contact is perpendicular to the tangent, so the triangle formed is right-angled. If radius is $r$, then $25^2 = 24^2 + r^2$. Thus $r^2 = 625 - 576 = 49$, so $r = 7\text{ cm}$. Options B, C and D do not satisfy the Pythagorean relation.