From a point $A$, the length of a tangent to a circle is $24$ cm and the distance of $A$ from the center is $25$ cm. The radius of the circle is

The tangent at any point on a circle is perpendicular to the radius at that point, creating a right triangle between the point A, the center O, and the tangent point. In this right triangle, the distance from A to the center is the hypotenuse of 25 cm, and the tangent is a leg of 24 cm. Using the Pythagorean theorem, the radius equals the square root of 25 squared minus 24 squared, which is the square root of 625 minus 576. The radius is the square root of 49, which equals 7 cm.

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