Final answer:
Using the Pythagorean theorem, we calculate the radius of the circle to be 7 cm by forming a right triangle with the given tangent and the distance from point P to the center of the circle. The radius is the side adjacent to the right angle in the triangle, and option A (7 cm) is the correct answer.
Step-by-step explanation:
To find the radius of the circle, we will use the properties of a right triangle formed by the radius, the tangent, and the line joining the center of the circle to the point P. According to the Pythagorean theorem, the sum of the squares of the lengths of the two shorter sides of a right triangle is equal to the square of the length of the longest side (hypotenuse).
In this scenario, the tangent line and the radius are perpendicular to each other, thus forming a right-angled triangle with the line from point P to the center being the hypotenuse. Given that the length of the tangent (opposite to the right angle) is 24 cm and the distance to the point P (hypotenuse) is 25 cm, we can set up the Pythagorean theorem as follows:
radius2 + 242 = 252
Solving for the radius:
radius2 + 576 = 625
radius2 = 625 - 576
radius2 = 49
radius = √49
radius = 7 cm
Therefore, the correct radius of the circle is option A, which is 7 cm.